Question

How do you evaluate the definite integral `int s^3-3s^2+2` from `[-2,2]`?

Answer 1

`-8`

Explanation:

Integrate each term using the `color(blue)"power rule for integration"`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(int(ax^n)=a/(n+1)x^(n+1))color(white)(2/2)|)))`

`rArrint_(-2)^2(s^3-3s^2+2)ds`

`=[1/4s^4-s^3+2s]_(-2)^2`

Evaluate for s = 2 and subtract the evaluation for s = - 2

`=(4-8+4)-(4+8-4)=0-8=-8`