Goal: Evaluate an iterated integral in two ways
Remember the Fubini's theorem concerning the double integral of a function of two variables f(x,y) that is continuous over a rectangular region R:
Then the double integral is an iterated that can be expressed as:
This means that a double integral can be integrated in two ways. First starting to integrate with respect to y and then x. Second, integrate with respect to x then y. In either way, we obtain the same result.
Example
Let's consider the function f(x, y) = 3x²- y over the rectangular region
Solution
Practice
Using the Fubini's theorem, evaluate the following integral in two ways:
Practice
