Last Updated 10/28/2022

Sage Essentials
Section 9: Vector Calculus

The integrate Command

Example 2

Evaluate ${\displaystyle \underset{1}{\overset{2}{\int }}{\displaystyle \underset{0}{\overset{1}{\int }}{x}^2{y}^{}dy}dx}$ .

Here is another way of evaluating the same integral.

This style emphasizes the order of integration. In this example, it is integrating w.r.t. y first, then w.r.t. x.

Try this!

Does it matter if we reverse the order of integration in the example above? Verify your answer.