Let and be continuous functions

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Let

f: \mathbb{R} \to \mathbb{R}

and

g: \mathbb{R} \to \mathbb{R}

be continuous functions, then the value of

\int_{-\pi/2}^{\pi/2} [f(x) + f(-x)][g(x) - g(-x)]\,dx

is equal to (1)

-1

(2)

0

(3)

1

(4) None of these