Question

What is the integral of this graph?

`2x^3+3x^2+4`

Answer 1

I got: `x^4/2+x^3+4x+c`

Explanation:

I think you mean:

`int(2x^3+3x^2+4)dx`

Here you want to find the Primitive `F(x)` (or anti-derivative) of your function; that is a function which, once derived, will give you your function.

We use the facts that:
1) the integral of `x^n` is `x^(n+1)/(n+1)`;
2) we can break the sum into single integrals;
3) we can take the constants out of the integral sign.
4) `intdx=intx^0dx=x`;

So we get:

`2intx^3dx+3intx^2dx+4intdx=`
`=2x^4/4+3x^3/3+4x+c=x^4/2+x^3+4x+c`

`c` is a constant we include to cover all the possibilities in the Primitive (we do not know if the Primitive had a constant in it because if it had been there it would have disappeared during derivation to get your function.