Purchase Solution

Moment of inertia and Change of variables

Not what you're looking for?

Ask Custom Question

Using the coordinate change u=xy, v=y/x, set up an iterated integral for the polar moment of inertia of the region bounded by the hyperbola xy=1 , the x-axis, and the two lines x=1 and x=2.
Choose the order of integration which make the limits simplest

I found something , I just want you to help on it : here is what I have:

the region is attached to the x axis...
so the polar momentum is iqual to:
double integral(y^2)dxdy
---->but y^2=u*v
AND the jacobian matrice of U... and v...
is equal to 2*y/x=2*v
so the inverse is 1/(2v)

"double integral(y^2)dxdy=(1/(2v))*uv.dvdu" right?

when x=1 and y=0 we get u=v
when xy=1 we get u=1
finally when x=2 then v=u/4 right?

so we see that we have

double integral(u/2)dudv, for u varying from 1 to v
and v varying from 1 to v, no?

My result then is "1/24(1-v^3)"

Purchase this Solution

Solution Summary

The solution demonstrates how to apply change of variables to a double integral, from the change in the integrand to the change in integration limits.
The solution contains 3 pages of completre derivations.

Solution Preview

Hello and thank you for posting your question to Brainmass!

The solution is attached below in two files. the files are identical in content, only differ in format. The first is in MS Word XP Format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you. ...

Purchase this Solution

Free BrainMass Quizzes
Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

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.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

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.