Integrating Over an Oval: Solving Double Integrals with Non-Circular Boundaries

In summary, the conversation is about how to integrate over the equation Z^2 = 4x^2 + y^2 with the plane z = 1. The person is trying to find the area of the curve and is unsure of how to double integrate the equation. They mention using polar coordinates but are unsure if it will work for an oval shape. They also mention using Stoke's theorem.
  • #1
rad0786
188
0
Anybody know how to integrate over...

Z^2 = 4x^2 + y^2 with the plane z = 1 ?

this comes from my class notes... hmmm.. the proff did some thing really messy... or at least i wrote it messy...

but i got

0(integral)2pi 0(integral)1 z dz d(pheta)

which doesn't seem to make sense since its an Oval, not a circle.

what would be the limits in polar coords?
 
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  • #2
I'm not sure what you're trying to do.

Are you trying to find the area of the curve

[tex]4x^2 + y^2 = 1[/tex]?
 
  • #3
yes.. i suppose its that... but the double integral.
infact, the question asks to find the line integral using stokes therm.

so... just how do you doulbe integrate that equation above? its an oval, so you cannot really use polar coords right?
 

1. What is a double integral?

A double integral is a mathematical concept used to calculate the volume under a surface in a two-dimensional space. It is represented by the symbol ∫∫, and involves evaluating the function at multiple points within a given region.

2. How is a double integral different from a single integral?

A single integral is used to calculate the area under a curve in a one-dimensional space, while a double integral is used to calculate the volume under a surface in a two-dimensional space. In a double integral, the function is integrated with respect to two variables, whereas in a single integral, it is integrated with respect to only one variable.

3. What is the purpose of a double integral?

The purpose of a double integral is to calculate the volume under a surface in a two-dimensional space. It is commonly used in physics, engineering, and other scientific fields to solve problems involving three-dimensional objects.

4. What are the different types of double integrals?

There are two types of double integrals: iterated integrals and double integrals with changing order of integration. Iterated integrals involve evaluating the function in one variable first, and then integrating the result with respect to the other variable. Double integrals with changing order of integration involve changing the order in which the variables are integrated, which can make the calculation easier in some cases.

5. How do you solve a double integral?

To solve a double integral, you first need to identify the region of integration and the limits of integration for each variable. Then, you can use one of the two types of double integrals to calculate the volume under the surface. The calculation involves evaluating the function at multiple points within the region of integration and adding up the results. This can be done using techniques such as Fubini's theorem or by using a double integral calculator.

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