Question

What is `f(x) = int (x+3)^2-2x dx` if `f(1) = 0`?

Answer 1

`f(x)=1/3(x+3)^3-x^2-61/3`

Explanation:

`f(x)=int(x+3)^2-2xdx`

Use `inth(x)+g(x)dx=inth(x)dx+intg(x)dx`
`f(x)=int(x+3)^2dx-int2xdx`
`f(x)=1/3(x+3)^3-x^2+C`

Evaluate the constant of integration
`0=1/3(1+3)^3-1^2+C`
`0=1/3(4)^3-1+C`
`0=64/3-3/3+C`
`0=61/3+C`
`C=-61/3`