Question

The area bounded by the curve f(x) = x + sin x and its inverse function between the ordinates x = 0 to x = 2p is-

• A. 4p sq. units
• B. 8p sq. units
• C. 4 sq. units
• D. 8 sq. units

Answer 1

Answer: (D)

8 sq. units

Answer 2

Required area = 4A

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

$\frac { \pi ^ { 2 } } { 2 } - \cos \pi + \cos 0 - \frac { \pi ^ { 2 } } { 2 }$ = 2 sq. units