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The value of the integral int3^6 sqrtx/(...

The value of the integral `int_3^6 sqrtx/(sqrt(9-x)+sqrtx)dx` is

A

`3/2`

B

2

C

1

D

`1/2`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `l=int_(3)^(6)(sqrtx)/(sqrt(9-x)+sqrtx)dx" …(i)"`
`=int_(3)^(6)(sqrt(9-x))/(sqrt(9-9+x)+sqrt(9-x))dx`
`rArr" "l=int_(3)^(6)(sqrt(9-x))/(sqrtx+sqrt(9-x))dx" …(ii)"`
On adding Eqs. (i) and (ii), we get
`2l=int_(3)^(6)1dx=[x]_(3)^(6)=6-3`
`rArr" "l=(3)/(2)`
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