Question

${\int }_{-\frac{\pi }{2}}^{\frac{\pi }{2}}\sqrt{\frac{1}{2}(1-cos2x)}dx=$

• A. 0
• B. 2
• C.
• D. None of these

Answer 1

The correct option is B

2

${\int }_{-\frac{\pi }{2}}^{\frac{\pi }{2}}\sqrt{\frac{1}{2}(1-cos2x)}dx=2{\int }_0^{\frac{\pi }{2}}|sinx|dx$
$=2[-cosx{]}_0^{\frac{\pi }{2}}=2[-cos\left(\frac{\pi }{2}\right)+cos0]=2$