Double Integral: Calculating Limits & Value

[Tayyabah]

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

 

[tiny-tim]

Welcome to PF!

Hi Tayyabah! Welcome to PF!

(I see you've discovered how to start a thread! )

∬_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 )

 

[Tayyabah]

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.

 

[tiny-tim]

(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!

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? ​