What is the integral of this graph?

#2x^3+3x^2+4#

1 Answer
Gió
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.

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