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Evaluate : int(0)^(1)(e^(sqrt(x)))/(sqrt...

Evaluate : `int_(0)^(1)(e^(sqrt(x)))/(sqrt(x))dx`

Text Solution

Verified by Experts

`"Let " sqrt(x) =t`
`rArr " "(1)/(2sqrt(2)) dx=dt`
`rArr " "(1)/(sqrt(x)) dx =2 dt`
` At x=0," "t=sqrt(0) =0`
` At x= 1 ," "t=sqrt(1) =1`
`:. int_(0)^(1) (e^(sqrt(x)))/(sqrt(x)) dx = int_(0)^(1) e^(t). 2dt =2[e^(t)]_(0)^(1)`
`=2(e^(1)-e^(0)) =2 (e-1) .`
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