Question

The value of ${\int }_{-2}^{2}cosec\left(cose{c}^{-1}x\right)dx$ is

• A. 1
• B. 0
• C. 4
• D. 2

Answer 1

Answer: (B)

0

Let $I={\int }_{-2}^{2}cosec\left(cose{c}^{-1}x\right)dx$
$I={\int }_{-2}^{-1}xdx+{\int }_{-1}^{1}0dx+{\int }_1^{2}xdx$
$I=(\frac{1}{2}-\frac{4}{2})+(\frac{4}{2}-\frac{1}{2})=0$
Since $cose{c}^{-1}x$ does not exist in $(-1,1)$