Question

Describe in words the surface whose equation is given.

\({\rm{\theta = \pi /4}}\).

Short answer

The described surface is a half plane.

Step-by-step solution

Concept Introduction

A multiple integral is a definite integral of a function of many real variables in mathematics (particularly multivariable calculus), such as f(x, y) or f(x, y) (x, y, z). Integrals of a two-variable function over a region

 Step 2:Explanation of the solution

Consider the equation we are given.

Since angle is fixed, it means that only two dimensions can vary.

These are \({\rm{r}}\) and \({\rm{z}}\).

This means that the surface is a vertical half plane since \({\rm{r > 0}}\)and \({\rm{z}}\) can be anything.