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…
Mathematics · JEE Main · NTA Exams — Integral Calculus
Let p(x) be a function defined on R such that \(\lim _{x \rightarrow \infty} \frac{f(3 x)}{f(x)}=1\)\(p^{\prime}(x)=p^{\prime}(1-x)\) for all \(x \in[0,1], P(0)=1\) and \(P(1)=41\). Then, \(\int_{0}^{1} p(x) d x\) equals
- 21
- 41
- 42
- \(\sqrt{41}\)
Answer
(A) 21
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- _ 0 ^ / 4 x x ^ 3 x d x equal to
- The solution for x of the equation _ 2 ^ x d t t t^ 2 -1 = 12 is
- 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…
- The value of I= _ -2 ^ 4 [x^ 3 +3 x^ 2 +3 x+3+(x+1) (x+1) ] d x equals
- 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…
- The value _ 1 n ^ 12 n-1 n x a-x + x 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…
- The value of the integral _ -a ^ a x e^ x^ 2 1+x^ 2 d x is,
More Integral Calculus questions · Browse all practice questions