Converting Cartesian to Polar Coordinates for a Double Integral

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Homework Help Overview

The discussion revolves around converting a double integral from Cartesian to polar coordinates. The original integral involves a region defined by specific limits in Cartesian coordinates, which raises questions about the conversion process and the implications of the region's boundaries.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between Cartesian and polar coordinates, particularly focusing on the expression for y in polar form. There is also a discussion about the implications of the limits of integration and how they translate into polar coordinates.

Discussion Status

The conversation includes attempts to clarify the expression for y in polar coordinates, with some participants suggesting specific forms and questioning the original setup. While one participant indicates they have solved the problem, the discussion remains open with various interpretations being explored.

Contextual Notes

Participants are working under the constraints of a homework problem that requires careful consideration of the limits of integration and the conversion process. The presence of a negative sign in the limits has been noted as a point of confusion.

CaptainEvil
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I'm working on a double integral and need to change from cartesian to polar coords.

The double integral in cartesian coords is
Double integral from 0 to a (in dy) and from -sqrt(a^2 - y^2) in dx (NOTE minus sign before sqrt)

the little minus sign is troubling. How would I convert this region into polar coords?
 
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I'm guessing your a is your radius? So what does y = ?
 
the whole question is

Double integral
(0 to a) (-sqrt(a^2 - y^2) to 0) of x^2y dxdy
 
Right, I'm asking you in polar coordinates, what does y =?
 
y = rsintheta

but I solved it, thanks anyway
 
Doesn't it equal a sin(theta) here?
 

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