Question

Find the definite integral `int_0^1dx/(2x-3)`?

Answer 1

`int_0^1dx/(2x-3)=-0.5493`

Explanation:

Let `u=2x-3`, hence `du=2dx` and

`intdx/(2x-3)=1/2int(du)/u=1/2lnu=1/2ln|2x-3|`

Hence, `int_0^1dx/(2x-3)`

= `1/2ln|2x-3|_0^1`

= `1/2ln|-1|-1/2ln|-3|`

= `1/2ln1-1/2ln3`

= `0-0.5493`

= `-0.5493`