Let $$f$$ and $$g$$ be two continuous functions. Then $$\int_{ - \frac{\pi }{2}}^{\frac{\pi }{2}} {\left\{ {f\left( x \right) + f\left( { - x} \right)} \right\}\left\{ {g\left( x \right) - g\left( { - x} \right)} \right\}} dx$$ is equal to :
A.
$$\pi $$
B.
1
C.
$$-1$$
D.
0
Answer :
0
Solution :
Clearly, $$f\left( x \right) + f\left( { - x} \right)$$ is an even function while $$g\left( x \right) - g\left( { - x} \right)$$ is an odd
function.
$$\therefore $$ the integrand is an odd function. So, $$I=0.$$
Releted MCQ Question on Calculus >> Application of Integration
Releted Question 1
The area bounded by the curves $$y = f\left( x \right),$$ the $$x$$-axis and the ordinates $$x = 1$$ and $$x = b$$ is $$\left( {b - 1} \right)\sin \left( {3b + 4} \right).$$ Then $$f\left( x \right)$$ is-