If `int_1^2e^x^2dx=a ,t h e nint_e^(e^4)sqrt(1n x)dxi se q u a lto` `2e^4-2e-a` (b) `2e^4-e-a` `2e^4-e-2a` (d) `e^4-e-a`

Options

A. `2e^(4)-2e-a`
B. `2e^(4)-e-a`
C. `2e^(4)-e-2a`
D. `e^(4)-e-a`

Answer

B

Explanation

`I_(1)=int_(e)^(r)sqrt(In x) dx`
Putting `t=sqrt(In x)` i.e. `dt=(dx)/(2x sqrt(In x))` we get
`dx=2te^(t^(2))dt`
or `int_(e)^(e^(4))sqrt(Inx)dx=int_(1)^(2) 2t^(2) e^(t^(2))dt`
`=te^(t^(2))|_(1)^(2)-int_(1)^(2) e^(t^(2))dt`
`=2e^(4)-e-a`