Question

please help!

Answer 1

Antiderivative means indefinite integral doesn't it?
\[\huge f(x)=20x^3-30x^2+8x-8\]
\[\huge \int\limits f(x)dx=\int\limits(20x^3-30x^2+8x-8)dx\]
\[\huge =5x^4-10x^3+4x^2-8x+C\]

Answer 2

Yes great thank you!
why its C in the end?

Answer 3

Do you know how to solve indefinite integrals?... When solving for indefinite integrals, you MUST always add a constant to the end, no matter what. You will get 0 marks if you don't.

Answer 4

Because when you differentiate:
\[\huge x^2\]
You get:
\[\huge 2x\]
But if you differentiate:
\[\huge x^2+2\]
where 2 is a constant. You also get
\[\huge 2x\]
So you must always put a constant because you don't know if there is a constant or not.