Question

What is `f(x) = int -x^2-4 dx` if `f(2) = -1`?

Answer 1

`f(x) = -1/3 x^3 - 4x + 29/3`

Explanation:

`intax^n dx =( ax^(n+1))/(n+1) + c : n ≠ -1`
where c , is the constant of integration , is the standard integral.

apply this to each 'term by term'

hence `int(-x^2 - 4 )dx = -1/3 x^3 - 4x + c`

using f(2) = - 1 , allows c to be calculated.

hence : `-1/3 (2)^3 - 4(2) + c = - 1`

`-8/3 - 8 + c = - 1 rArr c = -1 + 8 + 8/3 rArr c = 29/3`