Question

Let f : R →R and g : R →R be continuous functions. Then the value of $\int _ { - \pi / 2 } ^ { \pi / 2 }${f (x) + f (-x)} {g (x) – g (-x)} dx is

• A. π
• B. 1
• C. –1
• D. 0

Answer 1

Answer: (D)

0

Answer 2

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