Question

$\underset{0}{\overset{\pi /4}{\int }}\frac{x\cdot \sin x}{{\cos }^{3}x}dx$ equals to:

• A. $\frac{\pi }{4}+\frac{1}{2}$
• B. $\frac{\pi }{4}-\frac{1}{2}$
• C. $\frac{\pi }{4}$
• D. $\frac{\pi }{4}+1$

Answer 1

Answer: (B)

$\underset{0}{\overset{\pi /4}{\int }}x\tan x{\sec }^{2}xdx={\left(x\frac{{\tan }^{2}x}{2}\right)}_0^{\pi /4}-\underset{0}{\overset{\pi /4}{\int }}\frac{{\tan }^{2}x}{2}dx$
$=\frac{\pi }{4}-\frac{1}{2}$