The area of the region whose boundaries are defined by the curves y=2 cos x, y=3 tan x, and the y-axis is

Options

A. `1+3" In "((2)/(sqrt(3)))` sq. units
B. `1+(3)/(2)" In "3-3" In "2` sq. units
C. `1+(3)/(2)" In "3-"In "2` sq. units
D. `" In "3-" In "2` sq. units

Answer

B

Explanation

Solving 2 cos x = 3 tan x, we get
`2-2sin^(2)x=3 sin x or sin x =(1)/(2)or x =(pi)/(6).`

`"Required area "=overset(pi//6)underset(0)int(2 cos x -3tan x) dx`
`=2 sin x -3 log sec x |_(0)^(pi//6)=1-3" In " 2+(3)/(2)" In "3` sq. units