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`        Definite integral 1 to 2 e^x² dx = a then find definite integral e to e^4 (lnx)^1/2 dx`
7 years ago

510 Points
```										we have to find integral (lnx)1/2 lim e to e4 ....let it be I...
I= (lnx)1/2dx     lim e to e4
now put lnx =t
after differentiating we get
dx =et dt lim 1 to 4
now expression becomes
I= t1/2 .et dt             lim 1 to 4
now put t = u2 , dt =2udu
now I= 2u2 e^u2 du     lim 1 to 2
now replacing variable u with x
I= 2x2 e^x2 dx      lim 1to 2      ............1

a=e^x2 dx  lim 1 to 2           (given)
integrating RHS and taking 1 as first function
a =xe^x2 - 2x2 e^x2 dx    lim 1 to 2
putting value of I in above
we get I= xe^x2 -a    lim 1 to 2
I= 2e4 -e -a            ans

```
7 years ago
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