The value of the integral int (a)^(b) (...

The value of the integral ` int _(a)^(b) (sqrt(x)dx)/(sqrt(x)+sqrt(1+b-x))` is

A

`pi`

B

`1/2(b-a)`

C

`pi/2`

D

`b-a`

Text Solution

Verified by Experts

The correct Answer is:

B

Let `l=int_(a)^(b)(sqrtxdx)/(sqrtx+sqrt(a+b-x))" ...(i)"`
`therefore" "l=int_(a)^(b)(sqrt(a+b-x))/(sqrt(a+b-x)+sqrtx)dx" ...(ii)"`
On adding Eqs. (i) and (ii), we get
`2l=int_(a)^(b)dx=[x]_(a)^(b)=b-a`
`rArr" "l=(b-a)/(2)`

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The value of integral int_a^b (sqrtx dx)/(sqrtx +_ sqrt(a+b-x)) is :

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B

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C

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D

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