Module 4: Multiple Integrals

This module focuses on the physical interpretation of the double and triple integral.

In this module, I learned the difference between double integral and triple integral. Even though they are almost the same concepts, the difference between the two is that a double integral is used for integrating over a two-dimensional region, while a triple integral is used for integrating over a three-dimensional region.

One problem that was stuck in my mind in this classwork assignment would be item #2 in classwork assignment 2 which is regarding triple integrals. To discuss, Evaluate ∫∫∫ xb E dV where E is enclosed by z = 0, z = x + y + 5, x 2 + y 2 = 4 and x 2 + y 2 = 9.

Evaluating the problem, We will use cylindrical coordinates to easily solve this sum. Converting the given outer limits of E we get: z = 0, z = r cos θ + r sin θ + 5, r = 2 and r = 3. Since there is no limitation on the values of θ, we assume it has the values of 0 to 2π. This is also in accordance with the diagram which is obtained by drawing these surfaces. Also, we substitute x = r cos θ in the argument of the integral. Upon solving the problem, I find it challenging to arrive to the final answer since one must incorporate first the given variable for the first integral in order to arrive in solvinf for the second integral, and smae process would be applied in order to arrive in solving for the third integral, and answer after solving for it. I'm happy that I got to learn the past discussions regarding the integration formulas, because it helped me a lot in solving for these topics which is we can see in the solution itself that I answered the problem correctly arriving to the value of 65π/4.