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Question: Let f: R →R and g: R →Rbe continuous functions. Then the value of\(\int_{- \pi/2}^{\pi/2}{}\){f(x) +...

Let f: R →R and g: R →Rbe continuous functions. Then the value of∫−π/2π/2\int_{- \pi/2}^{\pi/2}{}{f(x) + f(–x)} {g (x) – g(–x)} dx is

A

π

B

1

C

–1

D

0

Answer

0

Explanation

Solution

Since h(x) = {f (x) + f(-x)} {g(x) – g (-x)} is an odd function, the value of the given integral is zero.