How do you evaluate the definite integral int logx dx from [2,4]?

1 Answer
Apr 30, 2018

I=6log2-2/ln10. See details below

Explanation:

I=intlogxdx Lets do it by parts u=logx and dv=dx

With this we have du=1/(xln10)dx and v=x

I=xlogx-int1/ln10dx=xlogx-1/ln10x=F(x)

F(4)-F(2)=4log4-4/(ln10)-2log2+2/ln10=4log4-2log2-2/ln10=4log2^2-2log2-2/ln10=6log2-2/ln10