How do you find the antiderivative of x^2+5x, if the point (0,5) exists on the graph of the antiderivative?

1 Answer
Oct 16, 2014

By integrating,

F(x)=int(x^2+5x)dx=1/3x^3+5/2x^2+C.

Since f(0)=5,

f(0)=1/3(0)^3+5/2(0)^2+C=C=5.

Hence,

F(x)=1/3x^3+5/2x^2+5.

I hope that this was helpful.