Question

The number of solutions of the equation ${\int }_{-2}^x|cosx|dx=0,xϵ(0,\frac{\pi }{2})$ is

• A. 1
• B. 2
• C. 3

Answer 1

${\int }_{-2}^x|cosx|dx={\int }_{-2}^{-\frac{\pi }{2}}|cosx|dx=+{\int }_{-\frac{\pi }{2}}^x|cosx|dx$
${\int }_{-2}^{-\frac{\pi }{2}}-cosxdx+{\int }_{-\frac{\pi }{2}}^{x}cosxdx$
$\Rightarrow 1-sin2+sinx+1=0$
$sinx=sin2-2<-1$
Which is not possible hence no solution in $(0,\frac{\pi }{2})$