Question

How do you evaluate the definite integral `int (x-1)^3dx` from [2,3]?

Answer 1

`int_2^3 (x-1)^3dx = 15/4`

Explanation:

`int_2^3 (x-1)^3dx = int_2^3 (x-1)^3d(x-1)`

`int_2^3 (x-1)^3dx = [(x-1)^4/4]_2^3`

`int_2^3 (x-1)^3dx = (3-1)^4/4 - (2-1)^4/4`

`int_2^3 (x-1)^3dx = (2^4/4-1/4)`

`int_2^3 (x-1)^3dx = (16/4-1/4) =15/4`