Question

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

Answer 1

`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`