functional integration???

Calculus Level 4

If f ( x ) f(x) be differentiable function in interval such that f ( x ) = f ( 10 − x ) f(x)=f(10-x) ,then the value of
∫ − 5 5 f ′ ( 5 + x ) x 4 e x 2 d x \displaystyle\int _{-5}^{5} {f'\left(5+x\right) { x }^{ 4 } } { e }^{ { x }^{ 2 } } dx


The answer is 0.

Mudit Bansal by mudit bansal , 25, India

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1 solution

Pranjal Jain
Jan 13, 2015

Substitute f ( x ) = 1 f(x)=1 , it satisfies given conditions. f ′ ( x ) = 0 f'(x)=0 . So the given integral would be 0 \boxed{0}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

@Mudit Bansal Slightly edited L a T e X LaTeX . Check it back for accuracy. Also added a dx

Pranjal Jain - 6 years, 5 months ago

Can you please explain ...

Aditya Sky - 4 years, 2 months ago

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