Question

The value of $I=\underset{-10}{\overset{3}{\int }}\mathrm{sgn}({\cot }^{-1}x+e^{-x}+1-\sin x)dx$ is

• A. $15$
• B. $19$
• C. $17$
• D. $13$

Answer 1

The correct option is D $13$

${\cot }^{-1}x>0,e^{-x}>0,1-\sin x\ge 0\forall x\in R$ $\Rightarrow I=\underset{-10}{\overset{3}{\int }}1\cdot dx=13$