Homework SourseFor the function gxlnex over the domain 01 where e is the ir
For the function g(x)=ln(ex) over the domain (0,1]. (where e is the irrational number e = 2.7182 .... not e^x ) evaluate the improper integral (lim of 0 to 1 ) of g(x) dx, showing all working
Solution
ln(ex) = 1 + lnx
=> lnx dx can be found out usin fg dx = gfdx - g\' fdx dx
Here f is 1 and g is ln x => lnx dx = x lnx - x => x (ln x -1) + c
Now 1 + ln x dx = x + xlnx - x + c=> xlnx + c is the answer
![For the function g(x)=ln(ex) over the domain (0,1]. (where e is the irrational number e = 2.7182 .... not e^x ) evaluate the improper integral (lim of 0 to 1 )](/WebImages/29/for-the-function-gxlnex-over-the-domain-01-where-e-is-the-ir-1082426-1761568647-0.webp "For the function g(x)=ln(ex) over the domain (0,1]. (where e is the irrational number e = 2.7182 .... not e^x ) evaluate the improper integral (lim of 0 to 1 )")
