Polar Integral Conversion Correct?

In summary, The conversation is about converting a double integral into polar coordinates. The person is unsure if they did the conversion correctly and asks for confirmation. The expert confirms that the conversion looks good, but points out a small error in the bounds of the inner integral in the first integral.
  • #1
bigedd1227
1
0
I'm not sure if I'm doing this conversion correctly. I have to convert the following double integral into polar. The integration part I can do, I just want to make sure I converted correctly. And sorry about the formatting bc I don't kno how to do the math formatting.


Int(Int((x^2+y^2))dy)dx
the bounds on the outer integral are -1 to 1
the bounds on the inner integral are -sqrt(1-y^2) to sqrt (1-y^2)

now here is what I got converting it to polar

Int(Int(r^3)dr)dtheta
outer bounds = 0 to 2pi
inner bounds = 0 to 1

Did I do the conversion correctly?
Thanks for the help
 
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  • #2
Lookin' good, but in the first integral the bounds on the inner integral should be -sqrt(1-x^2) to sqrt (1-x^2).
 
Last edited:

FAQ: Polar Integral Conversion Correct?

What is a polar integral?

A polar integral is a type of integral used to find the area of a region bounded by a polar curve. Unlike traditional integrals, which use rectangular coordinates, polar integrals use polar coordinates (angle and radius) to describe the curve.

What is the difference between a polar integral and a regular integral?

The main difference between a polar integral and a regular integral is the coordinate system used. While regular integrals use rectangular coordinates (x and y), polar integrals use polar coordinates (angle and radius). This allows for a more efficient way to calculate the area of certain shapes, such as circles and spirals.

How do you set up a polar integral?

To set up a polar integral, you first need to determine the limits of integration, which are the angles that define the region you want to find the area of. Then, you need to convert the polar function into a form that can be integrated, usually by using trigonometric identities. Finally, you integrate the function from the lower limit to the upper limit to find the area.

What are some common applications of polar integrals?

Polar integrals are commonly used in physics and engineering to calculate the mass, center of mass, and moment of inertia of symmetric objects. They are also used in calculus to find the volume of 3D shapes and in statistics to calculate the probability density function of continuous random variables.

What are some tips for solving polar integrals?

Some tips for solving polar integrals include sketching the polar curve to visualize the region, using symmetry to simplify the integral, and converting the function into a simpler form using trigonometric identities. It's also important to pay attention to the limits of integration and to use the appropriate integration techniques, such as substitution or integration by parts.

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