Question

Let `f(x)=(sin^(2)pix)/(1+pi^(x)).` Then, `int[f(x)+f(-x)]dx` is equal to

Answer 1

Correct Answer - B
(b) `f(x)+f(-x)=(sin^(2)pix)/(1+pi^(x))+(sin^(2)(-pix))/(1+pi^(-x))`
`=(sin^(2)pix)/(1+pi^(x))+((sin^(2)pix)pi^(x))/(pi^(x)+1)`
`=sin^(2)pix=(1-cos 2pix)/(2)`
`therefore int[f(x)+f(-x)]dx=int[(1-cos 2pix)/(2)]dx`
`=(1)/(2)xx-(sin 2pix)/(4pi)+C`