Integral Calculus — practice questions

269 curated practice questions from Integral Calculus (Mathematics JEE Main, NTA Exams) — 173 easy, 43 medium, 53 hard. Every question includes the final answer free; step-by-step worked solutions with a free account.

• [3] ^ n x ^ n+6 x d x, n ~N is equal to
• Given below are two statements. Statement - 1: _ 0 ^ + y | x| d x=2 n+1- v where त E E and 0 v . Statement - 2: If f(x)…
• For 0<x< 2 , _ 1 / 2 ^ 1 / 2 x d( x) equals to
• e^ x (1-x)^ 2 (1+x^ 2 )^ 2 d x is equal to
• Given below are two statements. Statement - 1 : For any n ∈ N, we have _ 0 ^ | x x | d x 2 (1+ 1 2 + 1 3 + + 1 )…
• Let T > 0 be a fixed real number. Suppose f is a continuous function such that for all x ∈ R, f(x+T)=f(x) . If I= _ U ^…
• If . |_ n = _ 0 ^ / 4 ^ n x ^ 2 x d x, then . |_ 1 , . |_ 2 , . |_ 3 are in
• The difference between the greatest and least values of the function (x)= _ 0 ^ x (t+1) d t on [2, 3] is
• The value of _ 0 ^ -1 ( 2 x-1 1+x-x^ 2 ) d x is,
• cosec x ^ 2 (1+ x 2 ) d x is equal to
• I_ 1 = _ 0 ^ / 4 ^ 3 x d x and I_ 2 = _ 0 ^ / 4 ^ 5 x d x I_ 3 = _ 0 ^ / 4 ^ 1 / 2 x d x and I_ 4 = _ 0 ^ / 4 ^ 1 / 3 x…
• _ 4 ^ 3 4 d x 1+ x is equal to
• The integral _ -1 / 2 ^ 1 / 2 ([x]+ ( 1+x 1-x ) ) d x equals
• The area (in sq. units) of the smaller portion enclosed between the curves, x^ 2 +y^ 2 =4 and y^ 2 =3 x , is:
• If ^ 4 x x d x= 1 2 _ ( 1+ x 1- x )-g(x)+c where g(x) equals.
• If f(x) d x= (x) , then x^ 5 f (x^ 3 ) d x is equal to
• If f(x)= e^ x 1+e^ x , t_ 1 = _ f(-a) ^ f(a) x g[x(1-x)] d x and d_ 2 = _ f(-a) ^ f(a) g[x(1-x)] d x . Then, the value…
• The value of I= _ 0 ^ 2 ( x+ x)^ 2 1+ 2 x d x is,
• If (x)= _ 1 / x ^ x t^ 2 d t then ^ (x) is equal to
• The area bounded by the curves y= x, y= x and y- axis in first quadrant is –
• The area of the region bounded by the curve y= 1- x between x=0 and x= is :
• If f(x) d x=g(x)+C, then f^ -1 (x) d x is equal to
• If f(x)= [x^ 2 + ^ 2 x ] 1+x^ 2 ^ 2 x d x and f(0) = 0, then f(1) is
• Evaluate _ 1 E ^ E d x x( x)^ 1 / 3 .
• Let 5( )= (x, y): y^ 2 x_ 1 and A(α) is area of the region S(α). If for a , 0 < 4, A( ) : A(4) = 2 : 5, then equals:
• The value of the integral _ 0 ^ 2 |x^ 2 -1 | d x is,
• The value of the integral _ -2 ^ 2 ^ 2 x [ x ]+ 1 2 d x (where [x] denotes the greatest integer less than or equal to…
• _ n [ 1 n^ 2 ^ 2 1 n^ 2 + 2 n^ 2 ^ 2 4 n^ 2 + + 1 n ^ 2 1 ] equals
• Let d d x (F(x))= e^ x x , x>0 . If _ 1 ^ 4 2 e^ x^ 2 x d x=F(k)-F(1) . Then, one of the possible values of K is
• d( ) 1- ^ 2 is equal to
• Let f:[1,2] [0, ) be a continuous function such that f( x )=f[1- x ] for all x [-1,2] . Let R_ 1 = _ -1 ^ 2 x f(x) d x…
• The value of _ 1 ^ [7] 2 1 x (2 x^ 7 +1 ) d x is,
• If I _ n = _ 0 ^ / 4 ^ n d where n is a positive integer, then n (I_ n-1 +I_ n+1 ) is equal to
• Evaluate 1 ^ 3 x (x+x) d x, x n , n I .
• Evaluate the integral _ 1 ^ d x x+1 .
• The value of _ x 0 _ 0 ^ x^ 2 ^ 2 t d t x x is
• _ n _ r=1 ^ n 1 n e^ r n is :
• If f^ (x)=x- 1 x^ 2 and f(1)= 1 2 . Find f(x)
• The value of the integral _ 0 ^ (2 k x) x d x, when k I , is
• If g(x)= _ 0 ^ x ^ 4 t d t then g(x+ ) equals
• _ -1 ^ 3 ( ^ -1 x x^ 2 +1 + ^ -1 x^ 2 +1 x ) d x equals to
• _ 0 ^ / 2 ^ 5 ( x 2 ) x d x is equal to
• _ 0 ^ 1000 e^ x-[x] d x is equal to where [ ∙ ] denotes the greatest integer function.
• If _ 0 ^ / 2 d 9 ^ 2 +4 ^ 2 =k , then the value of k is :
• Given below are two statements. Let I_ n = _ 0 ^ / 4 ^ n x d x Statement - 1: 1 n+1 Statement - 2: I_ n +I_ n-2 = 1 n-1…
• x- x 1- x d x is equal to
• (x- 1 x )^ 3 d x,(x>0) equals
• _ 0 ^ x a^ 2 ^ 2 x+b^ 2 ^ 2 x d x is equal to
• Statement - 1: x x d x (x > 0) can not be evaluated. Statement - 2: Only differentiable functions can be integrated.
• ( 2^ x -5^ x 10^ x ) d x is equal to
• The value of _ 0 ^ | ^ 3 | d is,
• The integral d x x^ 2 (x^ 4 +1 )^ 3 / 4 equals:
• _ 0 ^ 2 x- x 1+ x x d x is equal to
• The value of _ 0 ^ 2 ( 4+3 x 4+3 x ) d x is,
• The value of _ 0 ^ 2 x ^ 2 x ^ 2 x+ ^ 2 x d x is equal to :
• The value of _ 0 ^ 1 x^ 4 +1 x^ 2 +1 d x is,
• x ^ e -1 + e ^ x -1 x ^ e + e ^ x d x is equal to
• The value of _ 0 ^ 0 [ ^ -1 x ] d x is
• The value of the integral _ 0 ^ x ( ^ 4 x ^ 4 x ) d x is
• Let f be a non-negative function defined on the interval [0, 1]. If _ 0 ^ x 1- (f^ (t) )^ 2 d t= _ 0 ^ x f(t) d t, 0 x…
• _ 0 ^ x d x a^ 2 ^ 2 x+b^ 2 ^ 2 x is equal to
• The value of the integral _ 1 ^ 2 f(x) f(x)+f ( 2 -x ) d x is,
• _ 0 ^ x d x (1+x) (1+x^ 2 ) is equal to
• Let f:[0, ) R and F(x)= _ 0 ^ x f(t) d t . If F [ x ^ 2 ]= x ^ 2 [1+ x ] , then f(4) equals
• A value of α such that _ 0 ^ m+1 d x (x+m)(x+m+1) = _ n ( 9 8 ) is:
• If 1-x^ 2 x^ 4 d x=A(x) ( 1-x^ 2 )^ m +C , for a suitable chosen integer m and a function A(x), where C is a constant…
• If _ x ^ 1 t^ 2 f(t) d t=(1- x) . then f ( 1 3 ) equals
• The area between the curves y= x and the line y=x+1 in the second quadrant is –
• The value of _ 0 ^ 2 x d x is,
• If [x] stands for greatest integer function the value of _ 4 ^ 10 [x^ 2 ] [x^ 2 -28 x+196 ]+ [x^ 2 ] d x ,
• If m is a non-zero number and x^ 5 m-1 +2 x^ 4 m-1 (x^ 2 m +x^ m +1 )^ 3 d x=f(x)+c then f(x) is
• The integral _ 2 ^ 4 x^ 2 x^ 2 + (36-12 x+x^ 2 ) d x is equal to:
• Let p(x) be a function defined on R such that _ x f(3 x) f(x) =1 p^ (x)=p^ (1-x) for all x [0,1], P(0)=1 and P(1)=41 …
• The area of the region described by A = (x, y) : x 2 + y 2 ≤ 1 and y 2 ≤ 1 – x is
• If f(x)= 2-x x 2+x x and g(x)= _ x x(x>0) then the value of the integral _ - / 4 ^ / 4 g(f(x)) d x
• The integral _ - 1 2 ^ 1 2 ([x]+ ( 1+x 1-x ) ) d x equals
• The value of _ -1 ^ 1 1+ x 1+x^ 2 d x is :
• d x 4 ^ 2 x+4 x x+5 ^ 2 x is equal to
• If ^ 4 x d x= ^ 3 x+ x+x+C then
• I_ 1 = _ 1 ^ 2 e^ x d x and I_ 2 = _ 1 ^ 2 _ e x d x Then
• Evaluate d x (1+x^ 2 ) 1-x^ 2
• Statement - 1: _ 0 ^ ^ 2 x ^ -1 t d t+ _ 0 ^ cas ^ 2 x ^ -1 t d t= 4 for all x. Statement - 2: d d x _ ^ (x) ^ |x| f(t)…
• Evaluate _ 0 ^ 2 x- x 1+ x x d x
• If f(x) is a function satisfying f ( 1 x )+x^ 2 f(x)=0 for all non-zero x, then _ n ^ 1 f(x) d x equals
• The value of _ -2 ^ 2 [a x^ 3 +b x+c ] d x depends on
• Let I= _ 0 ^ 1 x x d x and J= _ 0 ^ 1 x x d x . Then which one of the following is true?
• The value of ( 6 1+x^ 2 +10^ x ) d x is
• Given below are two statements. Statement - 1: The value of _ -4 ^ -5 (x^ 2 -3 ] d x+ _ -2 ^ -1 (x^ 2 +12 x+33 ) d x is…
• The value of _ -2 ^ 2 [p ( 1+x 1-x )+q ( 1-x 1+x )^ -2 +r ] d x depends on
• If f(x)=|x|+|x-1|+|x-2|, x R then _ 0 ^ 3 f(x) d x equals to
• _ - ^ 2 x(1+ x) 1+ ^ 2 x d x is
• The area bounded by the curves y = l n x, y = l n |x|, y = | l n x| and y = | l n| x || is
• The value of _ 0 ^ 2 z^ x z^ x +z^ x d x is,
• Evaluate _ 0 ^ 1 ( 1 x -1 ) d x .
• If _ 1 ^ 2 d x (x^ 2 -2 x+4 )^ 3 2 = k k+5 , then k is equal to:
• _ 0 ^ 2 x ^ 2 x ^ 2 x d x is equal to
• Let f : R R be a continuous function. Then _ x / 4 4 _ 2 ^ ^ 2 x f(x) d x x^ 2 - ^ 2 16 is equal to
• The value of _ - ^ ^ 2 x 1+a^ x d x, a>0 is,
• Evaluate (x^ 2 + 1 x^ 2 )^ 3 d x .
• Let I= _ 0 ^ 1 x x d x and J= _ 0 ^ 1 x x d x Then which one of the following is true ?
• Let y= x ^ [x] where x denotes the fractional part of x [x] denotes greatest integer x then _ 0 ^ 3 y d x=
• Evaluate _ 0 ^ ^ 2 m x ^ 2 m+1 x d x, m Z
• The value of _ 0 ^ / 2 ^ 1 x x+ x d x is:
• The value of _ -a ^ a [ ^ -1 x- ^ -1 1-x^ 2 ] d x , (a > 0) where _ i ^ a ^ -1 x d x=A is
• The area bounded between the parabolas x 2 = y 4 and x 2 = 9y and the straight line y = 2 is.
• [x^ 4 -x ]^ 1 / 4 x^ 5 dx is equal to
• The value of integral _ 0 ^ x f( x) d x is,
• If f ( 3 x-4 3 x+4 )=x+2, x - 4 3 and f(x) d x=A |l-x|+E x+C , then the ordered pair (A, B) is equal to :(where c is a…
• The value of _ - 2 ^ 2 (x^ 3 +x x+ ^ 5 x+1 ) d x is equal to
• If S_ n = [ 1 2 n + 1 4 n^ 2 -1 + 1 4 n^ 2 -4 + + 1 3 n^ 2 +2 n-1 ] then _ n S_ n is equal to
• If f(x)= _ 1 ^ x^ 3 d t 1+t^ 4 then f^ (x) is equal to
• The area enclosed between the curve y = log e (x + e) and the coordinate axes is
• If (x)= _ 1 x ^ x [t^ 2 ] d t_ 1 then ^ (1) is equal to
• Area of the region bounded by the curve y^ 2 =4 x, y- axis and the line y=3 is :
• The value of _ 0 ^ 2 d x 1+ ^ 3 x is,
• Given below are two statements. STATEMENT - 1: x^ 9 / 2 1+x^ 11 d x is equal to 2 11 |x^ 11 / 2 + 1+x^ 11 |+c STATEMENT…
• If x d x ^ 1 x (1+ ^ 5 x )^ 2 / 3 =f(x) (1+ ^ 5 x )^ 1 / a +c where c is a constant of integration, then f ( 3 ) is…
• The value of _ 1 ^ 2 d x x (1+x^ 4 ) is,
• Evaluate _ 0 ^ 5 (2+3 x^ 2 ) 3 x d x .
• The area of the circle exterior to the parabola y^ 2 =6 x is :
• The value of _ - / 2 ^ / 2 d x [x]+[ x]+4 , where [t] denotes the greatest integer less than or equal to t, is:
• _ x 0^ + 1 x^ 3 _ 0 ^ x^ 2 t d t is equal to
• Given below are two statements. Statement - 1: Let m be any integer. Then, the value of I_ m = _ 0 ^ 2 mx x d x is zero…
• If x ^ 11 / 2 (1+ x ^ 5 / 2 )^ 1 / 2 dx = A (1+ x ^ 5 / 2 )^ 7 / 2 + B (1+ x ^ 5 / 2 )^ 5 / 2 + C (1+ x ^ 5 / 2 )^ 1 /…
• The value of the integral _ -a ^ a x e^ x^ 2 1+x^ 2 d x is,
• The area (in square units) bounded by the curves y= x , 2 y-x+3=0, x-axis and lying in the first quadrant is
• Evaluate x +2 ( x ^ 2 +3 x +3 ) x +1 dx
• ( ^ -1 x )^ 3 1-x^ 2 d x is equal to
• Let f(x)= _ a ^ x g(t) d t , where g is a non-zero even function. If f(x+5)=g(x) , then _ a ^ f(t) d t equals
• _ 0 ^ 10 e ^ x-[x] d x ([ ] denotes GIF) is equal to
• If [ ] denotes the greatest integer function, then the integral _ 0 ^ [ x] d x is equal to:
• The value of _ 0 ^ 2 [ 2 x(1+ 3 x)] d x , where [t] denotes the greatest integer function is:
• The integral _ / 6 ^ / 3 ^ 2 / 3 x cosec ^ 4 / 1 x d x is equal to:
• The value of the _ n [ 1 n^ 2 + 1 n^ 2 -1 + 1 n^ 2 -2^ 2 + + 1 n^ 2 -(n-1)^ 2 ] is
• If _ 0 ^ f [ ^ 2 x ] d x=K _ 0 ^ f [ ^ 2 x ] d x , then the value of K is where (n Z)
• The value of the integral _ 1 / 3 ^ 3 (x+ 1+x^ 2 ) d x is
• Given below are two statements. Statement - 1: _ 0 ^ 1- ^ 2 x d x=0 Statement - 2: _ 0 ^ x d x=0 In the light of the…
• ( x-1) 1+( x)^ 2 ^ 2 dx is equal to
• Let A = (x, y) : y 2 - 4 . The area (in square units) of the region A is
• The smallest interval [ a , ~b ] such that _ 0 ^ 1 1 1+x^ 4 d x [a, b] . is given by
• Let f be a positive function. Let A_ 1 = _ 1-k ^ k x f[x(1-x)] d x and A_ 2 = _ 1-k ^ k f[x(1-x)] d x , where 2 k-1>0 …
• Let I_ n = _ 0 ^ / 4 ^ n x d x then 1 I_ 2 +I_ 4 , 1 I_ 3 +I_ 5 , 1 I_ 4 +I_ 6 , are in
• The value of 2 x (x- 4 ) d x is,
• Evaluate _ 0 ^ 2 x 1+ x d x .
• ^ -1 x 1-x d x equals
• _ - 3 ^ 3 x x ^ 2 x d x is,
• If a_ n = _ / 4 ^ / 2 ^ n x d x then a_ 2 +a_ 4 , a_ 3 +a_ 5 , a_ 4 +a_ 6 are in
• If the variables and are connected by the relation x= _ 1 ^ y d z 1+6 z^ 3 , then d^ 2 y d x^ 2 is proportional to
• Value of x satisfying _ 0 ^ 2[x+14] x 2 d x= _ 0 ^ x [x+14] d x is, where [ ] and denotes the greatest integer function…
• If f(y)=e^ y . g(y)=y: y>0 F(t)= _ 0 ^ t f(t-y) g(y) d y , then
• _ ^ [ x] d x . where [ . ] denotes the greatest integer function, is equal to
• The area of the region bounded by the curves y = |x–1| and y = 3 – |x| is
• ^ 3 x ^ 2 x+ x d x is equal to
• _ 0 ^ 2 [x^ 2 ] d x where [ . ] is GIF is :
• Let n ≥ 2 be a natural number and 0< < 2 . Then ( ^ n - )^ 1 / n ^ n+1 d is equal to:(where C is a constant of…
• If f(x) is defined on [-2,2] by f(x)=4 x^ 2 -3 x+1 and g(x)= f(-x)-f(x) x^ 2 +3 then _ -2 ^ 2 g(x) d x is equal to
• The value of I= _ -2 ^ 4 [x^ 3 +3 x^ 2 +3 x+3+(x+1) (x+1) ] d x equals
• If _ 1 = _ 1 ^ 1 2^ x^ 2 d x i_ 2 = _ 1 ^ 1 2^ x^ 3 d x . H_ 1 = _ 1 ^ 2 z^ x^ 2 d x, 4= _ 1 ^ 2 z^ x^ 3 d x , then
• Find the solution of differential equation d y d x = ^ 3 x 5 in ^ 4 x+x 2 x+1 :
• The value of the integral _ a ^ b x d x x + a+b-x is,
• Evaluate _ 0 ^ 2 x 1+ ^ 2 x d x .
• Let d d x F(x) = ( e^ x x ), x>0 . If _ 1 ^ 4 3 x e^ x^ 3 d x=F(k)-F(1) , then one of the possible value of k is
• If f (x) is differentiable and _ 0 ^ t^ 2 x f(x) d x= 2 5 t^ 5 , then f ( 4 25 ) is equal to
• The value(s) of _ 1 ^ 1 x^ 4 (1-x)^ 4 1+x^ 2 d x is (are),
• is equals to
• The value of the integral I= _ 0 ^ 1 x(1-x)^ n d x is:
• Let f( x )=f( x )+f ( 1 x ) . where f(x)= _ 1 ^ x t 1+t d t . Then, F(e) equals
• The integral _ 0 ^ 1+4 ^ 2 x 2 -4 x 2 d x equals :
• The value of I= _ 2 ^ 3 x 5-x + x d x will be
• Let function F be defined as F(x)= _ 1 ^ x e^ t t dt, x > 0 then the value of the integral _ 1 ^ x e ^ t t + a dt …
• x^ 3 +3 (x+1) (x^ 2 +1 ) d x equals.
• The area of the region bounded by the curve y=x x between x=0 and x=2 π is :
• Evaluate the following d x 2 a x-x^ 2
• _ 0 ^ x f(t) d t=x+ _ x ^ 1 t f(t) d t , then the value of f(1) is
• If f(x)=A ( x 2 )+E and f^ ( 1 2 )= 2 and _ 0 ^ 1 f(x) d x= 2 A , then constants A and B are
• If _ 1 and _ 2 be respectively the smallest and the largest values of in (0,2 )-( ) which satisfy the equation, 2 ^ 2 …
• The integral _ 0 ^ 1 2 (1+2 x) 1+4 x^ 2 d x equals:
• ^ 6 x+ ^ 6 x ^ 2 x ^ 2 x d x is equal to
• If A_ 1 = _ x ^ 1 1 1+t^ 2 d t and A_ 2 = _ 1 ^ 1 x 1 1+t^ 2 d t for x>0 , then
• The value of the integral _ 3 ^ 5 x 9-x + x d x is,
• Let f : R → R and g : R → R be continuous functions. Then, the value of the integral _ - 2 ^ 2 [f(x)+f(-x)][g(x)-g(-x)]…
• e^ x ( 1+ x 1+ x ) d x is equal to
• If for every integer n_ 1 _ ^ +1 f(x) d x=n^ 2 , then the value of _ -2 ^ 4 f(x) d x is
• If 1 (3-5 x)(2+3 x) = A 3-5 x + B 2+3 x , then A : B is
• Evaluate (x^ 2 +z^ x + z x +2 x ) d x .
• _ - 2 ^ 2 ^ 2 x ^ 5 x d x equals
• Let f(x) be a non-negative continuous function such that the area bounded by the curve y = f(x), x-axis and the…
• Given below are two statements. Statement - 1 : _ 0 ^ [x] 4^ x-[x] d x= 3[x] 2 2 Statement - 2 : _ 1 ^ [x] a ^ x-[x] dx…
• Let l_ n = ^ n x d x,(n>1) . If l_ 4 +l_ 6 =a ^ 5 x+b x^ 5 +c , where C is a constant of integration, then the ordered…
• x^ 2 +1 [ [x^ 2 +1 ]-2 x ] x^ 4 d x is equal to
• Evaluate 2 x- 2 x- x d x .
• The integral _ 4 ^ 3 4 d x 1+ x is equal to
• Area bounded by the curve y=x^ 3 , the x- axis and the ordinates x=-2 and x=1 is :
• Evaluate (1-x x) x (1-x^ 3 e^ 3 5 x ) d x .
• Evaluate _ 4 ^ 2 - 1 x^ 2 ( 1 x ) d x .
• The area bounded by y = x 2 – 4 and x + y = 2 is
• The value of _ 0 ^ d x (1+x)^ 3 is:
• If _ 0 ^ x f( x) d x=A _ 0 ^ 2 f( x) d x , then A is
• Evaluate (2+ )(3+4 ) d .
• _ - 3 2 ^ - 2 [(x+ )^ 3 + ^ 2 (x+3 ) ] d x is equal to
• If f(x)= array cc e^ x x: & for |x| 2 2 & otherwise array then _ -2 ^ 3 f(x) d x . is equal to
• The value of x x d x will be
• The value of x^ 2 d x (x^ 2 +a^ 2 ) (x^ 2 +b^ 2 ) is
• The value of 2 x ~d x (x- 4 ) is
• Smaller area enclosed by the circle x^ 2 +y^ 2 =4 and the line x+y=2 is :
• Let f(x) be a function satisfying f^ ( x )=f( x ) with f(0)=1 and g(x) be a function that satisfies f(x)+g(x)=x^ 2 …
• The inequality _ 0 ^ 1 d x 1+x^ n >1- 1 n (n N) is true for
• 1+ ( x 4 ) d x is equal to
• _ - / 3 ^ / 3 x x ^ 2 x d x is :
• ^ 4 x ^ 8 x d x is equal to
• Statement - 1: The value of _ 0 ^ 2 ^ 99 x d x is 0 . Statement - 2: _ a ^ 2 a f(x) d x=2 _ a ^ a f(x) d x . if f(2…
• Evaluate [1- ^ n-2 x ] x+ x ^ n-2 x d x .
• Evaluate x^ 5 +3 x^ 4 +x^ 3 -2 x^ 2 +5 x+7 x^ 3 d x .
• The value of _ -1 ^ 3 [a x^ 5 +b x^ 3 +c x+k ] d x where a, b, c, k are constants, depends only on
• If _ 0 ^ x f(t) d t=x^ 2 + _ x ^ 1 t^ 2 f(t) d t then f^ ( 1 2 ) is:
• _ 5 ^ 3 x x + x d x is equal to
• The value of _ 0 ^ [x] z^ x z^ [x] d x is, where [ ∙ ] denotes the greatest integer function.
• 2 x- 2 x- d x is equal to
• _ - ^ ^ 4 x ^ 4 x+ ^ 4 x d x is equal to
• Evaluate x^ 8 (1-x^ 3 )^ 1 3 d x
• If the integral 5 x x-2 ~d x = x + a 1n |sin x – 2 cos x| + k, then a is equal to
• Let f:(0, ) R and F(x)= _ 0 ^ x f(t) d t If F [ x ^ 2 ]= x ^ 2 (1+ x ) . then f(4) equals
• 1+ x 1- x d x equals
• If _ ^ / 3 2 k d =1- 1 2 ,(k>0) , then the value of k is:
• Given below are two statements. Let F(x) be an indefinite integral of ^ 2 x Statement - 1: The function F(x) satisfies…
• _ 0 ^ / 4 x x ^ 3 x d x equal to
• The area of the region bounded by the curve y=x-x^ 2 , x- axis between x=0 and x=1 is :
• At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t…
• The value of _ -1 ^ 1 [ 1+x+x^ 2 - 1-x+x^ 2 ] d x is …
• Let d ~d ~F ( x )= ( e ^ x x ), x > 0. If _ 1 ^ 4 3 x e^ x^ 3 dx = F (k) – F(1), then one of the possible values of k is
• The integral ^ 2 x ^ 2 x ( ^ 3 x+ ^ 3 x )^ 2 d x equal to:
• Statement - 1: f(x) is symmetrical about x = 2, then _ 2-a ^ 2+a f(x) d x is equal to 2 _ 2 ^ 2+a f(x) d x . Statement…
• Evaluate 2 x a^ 2 ^ 2 x+b^ 2 ^ 2 x d x .
• For any natural number 'm', evaluate (x^ 3 m +x^ 2 m +x^ m ) (2 x^ 2 m +3 x^ m +6 )^ 1 m d x, x>0 .
• ^ -1 x (1-x^ 2 )^ 3 / 2 d x is equal to
• The value of _ 0 ^ [x] (x-[x]) d x is, where [ ∙ ] is the greatest integer function.
• The value of _ -2 ^ 3 |1-x^ 2 | d x is,
• For any integer n, the integral _ 0 ^ e^ [n x^ 2 x . ^ 3 (2 n+1) x d x has the value
• The value of the integral _ e^ -1 ^ e^ 2 | _ e x x | d x is,
• Given below are two statements. Statement - 1: If f(x)= _ 1 ^ x _ r t 1+t+t^ 2 d t then f(x)=f ( 1 x ) for all x > 0…
• The solution for x of the equation _ 2 ^ x d t t t^ 2 -1 = 12 is
• Given below are two statements. Statement - 1 : The value of the integral _ / 6 ^ / 3 d x 1+ x is equal to 6 …
• ^ n x ^ 2 x dx equals
• Evaluate 1- x x (1+ x) d x .
• _ 6 ^ 3 d x 1+ x is equal to
• d x is equal to
• The value of _ 0 ^ 1 [1+e^ -x^ 2 ] d x is ....
• Let f(x)=x-[x] , for every real number , where is the integral part of . Then _ -1 ^ 1 f(x) d x is:
• If f(x)= _ 0 ^ x t t d t then f^ (x) is
• If f( a + b +1- x )= f ( x ) , for all x, where a and b are fixed positive real numbers, then 1 (a+b) _ a ^ b x…
• e^ x e^ 2 x +5 e^ x +6 d x equals
• _ -3 / 2 ^ - / 2 [x+ )^ 3 + ^ 2 (x+3 ) dx is equal to
• _ 0 ^ 2 [x^ 2 ] d x , where [ ∙ ] denotes the greatest integer function.
• If y=f(x) makes positive intercept of 2 and 1 unit on x and y axes and encloses an area of 3 4 square unit with the…
• _ n [ 1 n + n^ 2 (n+1)^ 3 + n^ 2 (n+2)^ 3 + .+ 1 8 n ] is equal to
• The value of the integral _ 0 ^ e^ [n s^ 2 x . ^ 3 (2 n+1) x d x, n E I , is
• If I_ n = _ 1 ^ E ( x)^ n d x , then I_ n +n I_ n-1 is
• ( x +1)- x x ( x +1) d x is equal to
• If f^ (x)= ^ -1 ( x+ x),- 2 <x< 2 , and f(0) = 0, then f(1) is equal to:
• The area enclosed between the curves y 2 = x and y = |x| is
• Evaluate _ 1 ^ 1 x^ 2 d x .
• The absolute value of _ 10 ^ 11 x 1+x^ 1 d x is...
• _ 0 ^ 2 x x + x d x is equal to
• Given below are two statements. Statement - 1: 10 x^ 9 +10^ x _ r 10 10^ x + x ^ 1 l dx = |10^ x + x ^ 1 l |+ c…
• The value of _ 1 ^ a [ x ] f ´ (x) dx, a > 1, where [x] denotes the greatest integer not exceeding x, is
• The value _ 1 n ^ 12 n-1 n x a-x + x d x is ,
• If 1 [3] x+1 + x+1 d x=A-6 |(x+1)^ 1 6 +1 |+c , then A is equal to
• The value of integral y= _ 1 ^ x^ 2 -2 x^ 3 x^ 2 -1 d x is
• Let g(x)= _ 0 ^ x f(t) d t where f is such that 1 2 f(t) 1 for t [0,1] and 0 f(t) 1 2 for t [1,2] . Then, g(2) is…

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