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int0^9(dx)/(1+sqrt(x))...

`int_0^9(dx)/(1+sqrt(x))`

A

`(3-2log2)`

B

`(3+2log2)`

C

`(6-2log4)`

D

`(6+2log4)`

Text Solution

Verified by Experts

Put `x=t^(2)` and `dx=2t dt`.
`[x=0impliest=0]` and `[x=9impliest^(2)=9impliest=3]`
`:.I=int_(0)^(3)(2t)/((1+t))dt=int_(0)^(3){2-(2)/((1+t))}dt=[2t-2log(1+t)]_(0)^(3)=(6-2log4)`.
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