Question

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

Answer 1

`-5/2, or, -2.5`.

Explanation:

Let `I=int_-3^2 (-x-1)dx`.

`:. I=-int_-3^2 (x+1)dx`

`=-[x^2/2+x]_-3^2`

`=-(2^2/2+2)+{(-3)^2/2+(-3)}`

`=-2-2+9/2-3`

`=-5/2, or, -2.5`.