Integrals in Higher Dimensions

This lecture delves into the concept of integrals in higher dimensions, focusing on the generalization of the Fubini's theorem to three dimensions. The instructor explains how to calculate volumes using double integrals and discusses the importance of changing the order of integration. Through detailed examples involving regions and cross-sectional areas, the lecture demonstrates the versatility of integration methods in various scenarios. The presentation concludes with a preview of change of variables in integrals, setting the stage for further exploration in subsequent sessions.