Evaluate the double integral by converting to polar coordinates

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Homework Help Overview

The problem involves evaluating a double integral by converting to polar coordinates. The original poster expresses uncertainty about converting the limits of integration and identifies the integrand as the square root of the sum of squares of the variables.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to understand how to convert the limits of integration and recognizes the geometric interpretation of the integrand. Some participants question the interpretation of the function under the square root and clarify the shape described.

Discussion Status

The discussion is ongoing, with participants exploring the correct interpretation of the function and its geometric implications. There is no explicit consensus yet, as participants are clarifying assumptions and definitions.

Contextual Notes

The original poster notes that the function involves a half-circle, which is under scrutiny for accuracy. There may be confusion regarding the correct representation of the limits of integration in polar coordinates.

alanthreonus
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Homework Statement


Convert to polar coordinates to evaluate

[tex]\int^{2}_{0}\int^{\sqrt(2x-x^2)}_{0}{\sqrt(x^2+y^2)}dydx[/tex]

The Attempt at a Solution



Really I'm just not sure how to convert the limits of integration. I know [tex]\sqrt(2x-x^2)[/tex] is a half-circle with radius 1, but I'm not really sure where to go from there.
 
Last edited:
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By √(2x-x) do you mean just √x ?
 
A half-circle with radius 1 would be y=sqrt(1-x^2), not what you wrote.
 
Woops, I meant sqrt(2x-x^2)
 

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