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Let f (x) be a twice differentiable func...

Let f (x) be a twice differentiable function defined on `(-oo,oo)` such that `f (x) =f (2-x)and f '((1)/(2 )) =f' ((1)/(4))=0.` Then
`int _(-1) ^(1) f'(1+ x ) x ^(2) e ^(x ^(2))dx` is equal to :

A

1

B

`pi`

C

2

D

0

Text Solution

Verified by Experts

The correct Answer is:
D
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VK JAISWAL-INDEFINITE AND DEFINITE INTEGRATION-EXERCISE (COMPREHENSION TYPE PROBLEMS)
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  3. Let f(x) be a non-constant twice differentiable function defined on (o...

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  7. Consider the function f (x) and g (x), both defined from R to R f (x...

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  8. Consider the function f (x) and g (x), both defined from R to R f (x...

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  9. Let f (x) be function defined on [0,1] such that f (1)=0 and for any ...

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  10. Let f (x) be function defined on [0,1] such that f (1)=0 and for any ...

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  11. Let f (x) be function defined on [0,1] such that f (1)=0 and for any ...

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  15. Let f :R to [(3)/(4), oo) be a surjective quadratic function with line...

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  16. Let g (x ) = x ^(C )e ^(Cx) and f (x) = int (0)^(x) te ^(2r) (1+3t ^(2...

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  17. Let g (x ) = x ^(C )e ^(Cx) and f (x) = int (0)^(x) te ^(2t) (1+3t ^(2...

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