Question

For $0 \leq x \leq \pi$ the area bounded by $y = x$ and $y = x + \sin x$ is

• A. 2
• B. 4
• C. $2 \pi$
• D. $4 \pi$

Answer 1

Answer: (A)

2

Answer 2

The curves $y = x$and $y = x + \sin x$ intersect at (0, 0) and $( \pi , \pi )$. Hence area bounded by the two curves

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

$= [ - \cos x ] _ { 0 } ^ { \pi } = - \cos \pi + \cos 0 = - ( - 1 ) + ( 1 ) = 2$.