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If f(x) and g(x) are two continuous func...

If f(x) and g(x) are two continuous functions defined on [-a,a] then the the value of `int_(-a)^(a) {f(x)f+(-x) } {g(x)-g(-x)}dx` is,

A

2a

B

f(a) g(a)

C

a

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
Clearly f(x)+f(-x) is an even function and g(x)+g(x) is an odd function.
`:. {f(x)+f(-x)}{g(x)-g(-x)}` is an odd function.
`rArr underset(-a)overset(a)int {f(x) +f(-x) }{g(x)-g(-x)}dx =0`
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