question_answer

If \[{{I}_{1}}=\int\limits_{0}^{\pi /2}{x\sin x\,\,dx}\] and \[{{I}_{2}}=\int\limits_{0}^{\pi /2}{x\cos x\,\,dx},\] then which one of the following is true?

A)  \[{{I}_{1}}+{{I}_{2}}=\frac{\pi }{2}\]

B)  \[{{I}_{1}}=\frac{\pi }{2}{{I}_{2}}\]

C)  \[{{I}_{1}}+{{I}_{2}}=0\]                 

D)  \[{{I}_{1}}={{I}_{2}}\]

E)  None of these