Question

$\underset{0}{\overset{\pi /2}{\int }}\frac{\cos x\sin x}{1+\sin x}dx$ is equal to

• A. $\log 2-1$
• B. $-\log 2$
• C. $\log 2$
• D. $1-\log 2$

Answer 1

Answer: (D)

$\sin x=t$
$\underset{0}{\overset{\frac{\pi }{2}}{\int }}\frac{\cos x\sin x}{1+\sin x}dx$
$\Rightarrow \underset{0}{\overset{1}{\int }}\frac{t}{1+t}dt=1-\log 2$