What is the integral of this graph?

2x^3+3x^2+4

1 Answer
Apr 28, 2017

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.