Double Integrals: ∬xy(x + y) dx dy over the region bounded by the curves y = x² and y = x.
In this video, we will walk through how to find the value of the double integral ∬_R xy(x + y) dx dy, where R is the region bounded by the curves y = x² and y = x. This involves understanding the geometry of the region, setting up the appropriate limits for integration, and evaluating the double integral step by step. By the end of the video, you'll see how to apply integration techniques to solve this kind of problem, including using substitution and changing the order of integration. This is a great exercise in applying calculus to real-world shapes and regions!
