Question

Area bounded by y = f ^–1 (x), x = 0, y = $\frac { \pi } { 6 }$& y = $\frac { 5 \pi } { 6 }$ , where f(x) = x + sin x, is -

• A. 3 $\sqrt { 3 }$ + $\frac { \pi ^ { 2 } } { 3 }$
• B. 2 $\sqrt { 3 }$ + $\frac { \pi ^ { 2 } } { 3 }$
• C. $\sqrt { 3 }$ +$\frac { \pi ^ { 2 } } { 3 }$
• D. $\frac { \pi ^ { 2 } } { 3 }$ –$\sqrt { 3 }$

Answer 1

Answer: (C)

$\sqrt { 3 }$ +$\frac { \pi ^ { 2 } } { 3 }$

Answer 2

y = x + sin x its inverse is given by x = y + sin y \ required area = $\int _ { \pi / 6 } ^ { 5 \pi / 6 } ( y + \sin y )$dy

= $\sqrt { 3 }$ + $\frac { \pi ^ { 2 } } { 3 }$