Double Integral: Calculating Limits & Value

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Homework Help Overview

The problem involves calculating a double integral of the function √(x² + y²) over a region D defined by the inequality x² + y² ≤ 2x. The discussion focuses on determining the limits of integration based on the given inequality.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss how to describe the shape of the region D to establish limits for the double integral. There is an exploration of modifying the inequality to better understand the region's geometry.

Discussion Status

The discussion is active, with participants providing insights into the geometric interpretation of the region D. One participant has identified the region as the interior of a circle, and there is ongoing exploration of how to set the limits of integration based on this understanding.

Contextual Notes

Participants are considering different approaches to express the limits of integration, including using x as a function of y and vice versa. There is an emphasis on ensuring the correct interpretation of the region defined by the inequality.

Tayyabah
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Homework Statement



I have to calculate the double integral given below.

Homework Equations



∬D√(x2 +y2) dxdy,D=x2+y2≤2x

The Attempt at a Solution



How can i calculate the limits from the give inequality to calculate the value of the given double integral?

Waiting for a kind response.

Thanks in advance
 
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Welcome to PF!

Hi Tayyabah! Welcome to PF! :smile:

(I see you've discovered how to start a thread! :wink:)
Tayyabah said:
∬D√(x2 +y2) dxdy,D=x2+y2≤2x

How can i calculate the limits from the give inequality to calculate the value of the given double integral?

first, describe (in words) the shape of D

(that should help you with the limits … alternatively, you may find that a change of coordinates would make it easier :wink:)
 
Thanks a bunch for prompt response.

If a modify the inequality representing D, it gets the following form

(x-1)2+y2≤ 1

Which means (If i am not wrong) D is representing the interior of a circle centered at (1,0) and having radius equal to 1.
 
Tayyabah said:
(x-1)2+y2≤ 1

Which means (If i am not wrong) D is representing the interior of a circle centered at (1,0) and having radius equal to 1.

That's right! :smile:

ok, now either have limits of x going from 0 to 2, and y as a function of x,

or y going from -1 to 0, and x as a function of y …

what do you get? :smile:​
 

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