Question

Find the antiderivative f(x) = x^2 +6x ― 8

Answer 1

Answer:
`(x^3)/(3) +3x^2-8x+C`

Explanation:

To find the antiderivative, it is essentially backwards derivative.

We have to split apart the given function.

`\int\limits {x^2+6x-8} \, dx` [break apart function into 3 separate antiderivatives]

`\int\limits {x^2} \, dx +\int\limits {6x} \, dx-\int\limits {8} \, dx` [antiderivative each part]

`(x^3)/(3) +3x^2-8x`

Notice that the problem didn't note a specific interval to find the antiderivative for, so we need to add the constant, C.

`(x^3)/(3) +3x^2-8x+C`