Use Coupon: CART20 and get 20% off on all online Study Material

Total Price: Rs.

There are no items in this cart.
Continue Shopping
Siddhant Agarwal Grade: 12

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

7 years ago

Answers : (1)

vikas askiitian expert
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
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies
  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: Rs. 15,900
  • View Details

Ask Experts

Have any Question? Ask Experts

Post Question

Answer ‘n’ Earn
Attractive Gift
To Win!!! Click Here for details