Question

How do you evaluate the integral of `int (2 -1/x)dx` from 1/2 to 3?

Answer 1

`int_(1/2)^3 (2-1/x)dx =5 - ln6`

Explanation:

Using the linearity of the integral:

`int_(1/2)^3 (2-1/x)dx = 2int_(1/2)^3dx - int_(1/2)^3 dx/x`

`int_(1/2)^3 (2-1/x)dx = 2(3-1/2) - (ln3-ln(1/2))`

`int_(1/2)^3 (2-1/x)dx =5 - ln6`