Question

The area of the bounded region by the curve y = sinx, the x-axis and the line x = 0 and x =$\pi$ is

• A. 4
• B. 2
• C. 0
• D. None of these

Answer 1

Answer: (B)

2

Answer 2

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

= $2 \int _ { 0 } ^ { \pi / 2 } \sin x d x$ = $2 [ - \cos x ] _ { 0 } ^ { \pi / 2 }$ = 2 [ $( - \cos \pi / 2 )$ – $( - \cos 0 )$]

= 2(1)

= 2 square unit.

Trick: For the curve $y = \sin x$ or $\cos x$ the area of $\int _ { 0 } ^ { \pi / 2 } \sin x d x = 1 , \int _ { 0 } ^ { \pi } \sin x d x = 2$ $\int _ { 0 } ^ { 3 \pi / 2 } \sin x d x = 3 , \int _ { 0 } ^ { 2 \pi } \sin x d x = 4$ and so on.