Question

What is ${\int }_{-\frac{\pi }{2}}^{\frac{\pi }{2}}xsinxdx$equal to ?

• A. 0
• B. 2
• C. -2
• D. $\pi$

Answer 1

The correct option is B 2

By intergration by part

${\int }_{-\frac{\pi }{2}}^{\frac{\pi }{2}}xsin\left(x\right)dx=–{\left|x\cos x\right|}_{-\frac{\pi }{2}}^{\frac{\pi }{2}}–{\int }_{-\frac{\pi }{2}}^{\frac{\pi }{2}}-\cos \left(x\right)dx=0+{\int }_{-\frac{\pi }{2}}^{\frac{\pi }{2}}\cos \left(x\right)dx={\left|\sin \right(x\left)\right|}_{-\frac{\pi }{2}}^{\frac{\pi }{2}}=1+1=2$