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int(a)^(b)(sqrt(x))/(sqrt(x)+sqrt(a+b-x)...

`int_(a)^(b)(sqrt(x))/(sqrt(x)+sqrt(a+b-x))dx=`. . . .

A

`a+b`

B

`(b-a)/(2)`

C

a-b

D

`(a-b)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `l=int_(a)^(b)(sqrt(x))/(sqrt(x)+sqrt(a+b-x))dx` . . . (i)
`=int_(a)^(b)(sqrt(a+b-x))/(sqrt(a+b-x)+sqrt(a+b-(a+b-x)))`
`l=int_(a)^(b)(sqrt(a+b-x))/(sqrt(a+b-x)+sqrt(x))` . . . (ii)
On adding Eqs. (i) and (ii), we get
`2l=int_(a)^(b)(sqrt(x)+sqrt(a+b-x))/(sqrt(x)+sqrt(a+b-x))dx`
`implies2l=int_(a)^(b)dx=(x)_(a)^(b)=b-a`
`impliesl=(b-a)/(2)`
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