Question

How do you evaluate the definite integral `int (x-2) dx` from [-1,0]?

Answer 1

`int_(-1)^0 (x-2)dx = - 5/2`

Explanation:

`int_(-1)^0 (x-2)dx = int_(-1)^0 (x-2)d(x-2)`

`int_(-1)^0 (x-2)dx = [(x-2)^2/2]_(-1)^0`

`int_(-1)^0 (x-2)dx = (0-2)^2/2 - ((-1)-2)^2/2`

`int_(-1)^0 (x-2)dx = 2 - 9/2`

`int_(-1)^0 (x-2)dx = - 5/2`