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Evaluate int(0)^((pi)/(2)) (sqrt(cotx))/...

Evaluate `int_(0)^((pi)/(2)) (sqrt(cotx))/( sqrt(cot x ) + sqrt( tan x )) dx `

A

`pi//4`

B

`pi//2`

C

`pi`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Let `I=int_(0)^(pi//2)(sqrtcotx)/(sqrt(cot)+sqrt(tanx))dx` . . .(i)
`rArrI=int_(0)^(pi//2)(sqrttanx)/(sqrt(cot)+sqrt(tanx))dx` . . .(ii)
On adding Eqs . (i) and (ii) , we get
` 2I=int_(0)^(pi//2)1dx`
`:. I=(pi)/(4)`
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