Question

The area of the region bounded by the curve y =$\frac { 1 } { 1 + ( \tan x ) ^ { 1 / 2 } }$ and the x-axis between the ordinates x = π/6 and x = π/3 is

• A. π/4
• B. π/2
• C. π/8
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

The given curve is y =$\frac { 1 } { 1 + ( \tan x ) ^ { 1 / 2 } }$

⇒ y =$\frac { ( \cos x ) ^ { 1 / 2 } } { ( \sin x ) ^ { 1 / 2 } + ( \cos x ) ^ { 1 / 2 } }$

Area bounded between the intervals x = π/6

and x = π/3 is given by

A =dx

= dx

= dx

Adding 2A =

⇒ A = $\frac { \pi } { 12 }$ sq. units