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The area of the region whose boundaries are defined by the curves `y=2cosx , y=3tanx ,a n dt h ey-a xi si s` `1+31n(2/(sqrt(3)))s qdotu n i t s` `1+3/2 1n3-31n2s qdotu n i t s` `1+3/2 1n3-1n2s qdotu n i t s` `1n3-1n2s qdotu n i t s`

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

Text Solution

Verified by Experts

The correct Answer is:
B
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
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