Integrali Doppi 03 - Calcolo di integrali doppi in coordinate polari

What if a domain is not normal with respect to either x or y? How do we use the reduction formula to calculate the double integral? There are essentially two solutions: 1) Divide the domain into suitable normal subdomains, calculate the integral over each of these domains, and add all the results. 2) Perform an appropriate change of variables so that the domain is normal in the new variables. In this video, you'll see the most common change of variables, which allows us to handle numerous situations where the domain, or the integrand, has some "circular" characteristics. Specifically, we'll focus on calculating double integrals in polar coordinates, which are very effective for calculating integrals over domains composed primarily of circular sectors or integrand functions that simplify greatly in their polar analytic form. By the end of the video, you'll have added a fundamental tool to your toolbox for calculating double integrals. Specifically, you'll have discovered both how to set up and solve a double integral in polar coordinates and how to "sniff out" that a certain integral is very likely easier to solve in polar coordinates. ______________________________________________________________ 🙏Thanks to Dr. FerruX for his valuable advice and support. / @DocFerruX Follow his channel for math content dedicated to the early years of high school. ______________________________________________________________ #️⃣Hashtag: #school #teaching #learning #study #teaching #learning #understanding #Mathematics #mathematicalanalysis #Algebra #calculus #maths #mathematics #math #numerical #limits #functions #infinities #infinitesimals #integrals #doubleintegrals #analysis2 #riemannintegral ______________________________________________________________ INDEX 00:00 Intro and channel objective 01:13 Polar coordinates: definition, relationship with Cartesian coordinates, and examples of effective use in describing domains and functions 07:24 Infinitesimal elements of area in polar coordinates 12:32 How to rewrite double integrals in polar coordinates 14:51 Example of calculating a double integral in polar coordinates 20:06 Outro