CUET Preparation Today
CUET
-- Mathematics - Section A
Definite Integration
The value of the integral e2∫e−1|logexx|dx, is
32
52
3
5
We have,
I=e2∫e−1|logexx|dx
⇒I=e2∫1/e|logex|xdx
⇒I=1∫1/e|logex|xdx+e2∫1|logex|xdx
⇒I=−1∫1/elogexxdx+e2∫1logexxdx
⇒I=−1∫1/elogexd(logex)+e2∫1logexd(logex)
⇒I=−[12(logex)2]11/e+[12(logex)2]e21
⇒I=−[12×0−12]+[12×4−0]=12+2=52