Q 14. - Calculus

Question

The volume increment $dV=---$ when you use cylindrical coordinates to evaluate a triple integral. Why is this the standard order of integration for cylindrical coordinates?

Step-by-Step Solution

Answer

The volume increment is $rdrdzd\theta$.

Step 1: Given Information

It is given that we need to evaluate volume increment by using cylindrical coordinates.

Step 2: Explanation

Mathematically we can write,

$\int \int \int f\left(r,\theta ,z\right)dV=\int \int \int f\left(r,\theta ,z\right)rdzdrd\theta$

Comparing we get,

$dV=rdzdrd\theta$

For simplest order of integration $r$ is expressed in terms of $\theta$