Question

Let $F\left(x\right)={\int }_0^x\frac{cost}{(1+t^2)}dt,0\le x\le 2\pi$. Then

• A. F is increasing in $(\frac{\pi }{2},\frac{3\pi }{2})$ and decreasing in $(0,\frac{\pi }{2})$ and $(\frac{3\pi }{2},2\pi )$.
• B. F is increasing in $(0,\pi )$ and decreasing in $(\pi ,2\pi )$.
• C. F is increasing in $(\pi ,2\pi )$ and decreasing in $(0,\pi )$.
• D. F is increasing in $(0,\frac{\pi }{2})$ and $(\frac{3\pi }{2},2\pi )$ and decreasing in $(\frac{\pi }{2},\frac{3\pi }{2})$.

Answer 1

The correct option is D F is increasing in $(0,\frac{\pi }{2})$ and $(\frac{3\pi }{2},2\pi )$ and decreasing in $(\frac{\pi }{2},\frac{3\pi }{2})$.