Confused about polar integrals and setting up bounds

In summary, the conversation discusses the process of subtracting two surfaces and determining the appropriate coordinate system for integration. The first surface is a sphere and the second surface is a cylinder, leading to the question of what volume of the sphere is outside the volume of the cylinder. The need to consider cross sections and possibly draw a figure is mentioned to determine the appropriate coordinate system.
  • #1
38
4
Homework Statement
I am trying to find the volume between y = x^2+z^2 and y = 3-4x^2-2y^2.
Relevant Equations
x^2+y^2+z^2 = p^2
z^2+y^2 = r^2
So I want to subtract the two surfaces, right? I really don't know where to start... I am guessing this would be some sort of triple integral, however I am very confused with the bounds.
Any help would be greatly appreciated!
Thanks!!
 
Last edited:
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  • #2
I assume the 3rd line, where z=8-x^2-x^2 has a mistake? Also, please write your equations in Latex.
 
  • #3
WWGD said:
I assume the 3rd line, where z=8-x^2-x^2 has a mistake?
I don't see a 3rd line or this equation. Likely the OP deleted it.
 
  • #4
Mark44 said:
I don't see a 3rd line or this equation. Likely the OP deleted it.
I think the problem statement was edited.
 
  • #5
The first surface is a sphere. The second surface is a cylinder. So I am guessing that p2>r2 and the question is actually what volume of the sphere is outside the volume of the cylinder.

Is this correct?
Given this geometry, which type of coordinate system (cartesian, cylindrical or spherical) is appropriate for integration and why? Hint: think about cross sections. You might want to draw a figure.
 

1. What are polar integrals and how do they differ from regular integrals?

Polar integrals are integrals that are used to calculate the area under a curve in polar coordinates. They differ from regular integrals in that they use polar coordinates (r, θ) instead of Cartesian coordinates (x, y) to represent points on a graph.

2. How do I set up bounds for a polar integral?

To set up bounds for a polar integral, you need to determine the limits for both the radius (r) and the angle (θ). The radius limits are typically given by the equation of the curve, while the angle limits are determined by the starting and ending points of the curve on the polar graph.

3. What is the purpose of using polar coordinates in integrals?

Polar coordinates are often used in integrals when dealing with curves that have a circular or symmetrical shape. This is because polar coordinates make it easier to express the relationship between the radius and the angle of a point on the curve, making the integration process simpler.

4. What are some common mistakes to avoid when working with polar integrals?

Some common mistakes to avoid when working with polar integrals include forgetting to convert the integrand to polar form, using the wrong limits for the radius and angle, and forgetting to include the "r" term in the integrand when calculating the area.

5. How can I practice and improve my understanding of polar integrals?

One way to practice and improve your understanding of polar integrals is to work through practice problems and examples. You can also try visualizing the polar curves and their corresponding integrals on a graphing calculator or online graphing tool. Additionally, seeking help from a tutor or attending a workshop on polar integrals can also be beneficial.

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