Determine the antiderivative of $f(x)=x^4-10x^3+5000$.

Primary tabs

Lesson Parent: 
Chapter 26 - Antiderivatives
Problem: 

Determine the antiderivative of $f(x)=x^4-10x^3+5000$.

Answer: 

$F(x)=\frac{1}{5}x^5-\frac{10}{4}x^4+5000x+C$

Solution: 

This is a polynomial so we can use Antiderivative Rule 5 to find its antiderivative. Applying the rule we see that
\[
F(x)=\frac{1}{5}x^5-\frac{10}{4}x^4+5000x+C
\]
where $C$ is the constant of integration.