Purchase Solution

Triple Integrals : Finding Volume of Solids with Boundaries

Not what you're looking for?

Ask Custom Question

1) Evaluate the triple integral e^(1-(x^2)-(y^2)) dxdydz with T the solid enclosed by z=0 and z= 4-(x^2)-(y^2)

2) Find the volume of the solid bounded above and below by the cone (z^2) = (x^2) + (y^2), and the side by y=0 and y= square root(4-(x^2)-(z^2))

Purchase this Solution

Solution Summary

A triple integral is evaluated, and the volume of a solid is obtained.

Solution Preview

Please see the attached file for the complete solution.
Thanks for using BrainMass.

a) We want to solve:

Well, the form x^2+y^2 leads us to this fact that the change of variables as x=r*cos(Ө), y=r*sin(Ө) and z=z could be useful. Because there have been no words on the limits of x and y, we consider 0≤Ө≤2п and 0≤r<∞ to cover the entire space. Then we naturally have: 0≤z≤(4-r^2)
We also have to consider that the jacobian of this change of variables is r. ...

Purchase this Solution

Free BrainMass Quizzes
Probability Quiz

Some questions on probability

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.