If _ 0 ^ x f(t) d t=x^ 2 + _ x ^ 1 t^ 2 f(t) d t then f^ ( 1 2 ) is:

Mathematics · JEE Main · NTA Exams — Integral Calculus

1. \(\frac{16}{25}\)
2. \(\frac{6}{25}\)
3. \(\frac{24}{25}\)
4. \(\frac{4}{5}\)

Answer

(B) 6 25

Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.

Related practice questions

• If f^ (x)= ^ -1 ( x+ x),- 2 <x< 2 , and f(0) = 0, then f(1) is equal to:
• _ -3 / 2 ^ - / 2 [x+ )^ 3 + ^ 2 (x+3 ) dx is equal to
• The area (in sq. units) of the smaller portion enclosed between the curves, x^ 2 +y^ 2 =4 and y^ 2 =3 x , is:
• 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
• The integral _ 0 ^ 1 2 (1+2 x) 1+4 x^ 2 d x equals:
• 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…
• Evaluate 2 x a^ 2 ^ 2 x+b^ 2 ^ 2 x d x .
• At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P…

More Integral Calculus questions · Browse all practice questions