Question

a>0, ${\int }_{-\pi }^{\pi }\frac{si{n}^{2}x}{1+a^x}dx=$

• A. π/2
• B. π
• C. aπ/2
• D. aπ

Answer 1

The correct option is A

π/2

$I={\int }_{-\pi }^{\pi }\frac{si{n}^{2}x}{1+a^n}dx={\int }_{-\pi }^{\pi }\frac{a^{n}si{n}^{2}x}{1+a^n}dx$
$\Rightarrow I={\int }_0^{\pi }si{n}^{2}dx=\frac{\pi }{2}$