How to Calculate a Volume Bounded by Two Surfaces Using Polar Coordinates скачать в хорошем качестве

How to Calculate a Volume Bounded by Two Surfaces Using Polar Coordinates

Calculating volumes bounded by surfaces are very common questions in advanced College Entrance Exams (GRE, JEE etc) and the standard way of answering them is to establish the bounded area in the x-y plane and then double integrate z=f(x,y) over that area. Sometimes however, especially when the area is a circle, it is far easier to double integrate r dr dθ with respect to r and θ in polar coordinates, rather than dxdy. That proves to be the case in this example, which we attack using two methods, firstly calculating the volume above and below the circle separately and secondly, doing the whole lot as one big integral. This video is part of the Gresty Academy podcast 'A Crash Course in Volumes Bounded by Surfaces' which can be watched at    • A Crash Course in Volumes Bounded by Surfaces   Join the Gresty Academy YouTube channel to get access to perks:    / @grestyacademy