Integral using the antiderivative

Problem

Compute $\displaystyle\int_0^2 x^3\,dx$ using the antiderivative.

Solution

An antiderivative of $x^3$ is $\dfrac{x^4}{4}$. Evaluating at the endpoints: $\int_0^2 x^3\,dx = \left[\frac{x^4}{4}\right]_0^2 = \frac{16}{4}-0 = \boxed{4}.$

Links

Topics: Integral
Concepts: Definite integral · Antiderivative
Skills: Compute · Integrate
Exercise types: Integral computation