Question

$\int _ { 0 } ^ { \pi } x \sin x d x =$

• A. $\pi$
• B. 0
• C. 1
• D. $\pi ^ { 2 }$

Answer 1

Answer: (A)

$\pi$

Answer 2

$I = \int _ { 0 } ^ { \pi } x \sin x d x = \int _ { 0 } ^ { \pi } ( \pi - x ) \sin x d x$

⇒ $2 I = \pi \int _ { 0 } ^ { \pi } \sin x d x = \pi [ - \cos x ] _ { 0 } ^ { \pi } \Rightarrow I = \pi$.