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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
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