xy coordinates to polar coordinates for double integral. hepl please!


by Andrew123
Tags: coordinates, double, hepl, integral, polar
Andrew123
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#1
Jan31-09, 02:08 AM
P: 25
1. The problem statement, all variables and given/known data
ok change the region R = { (x,y) | 1 <= X^2 + y^2 <= 4 , 0 <= y <= x } to polar region and perform the double integral over region R of z=arctan(y/x)dA


2. Relevant equations
r^2 = x^2 + y^2, x = r*sin(@), y = r * cos (@)


3. The attempt at a solution

i got R = { (rcos(@), rsin(@) | 1 <= r <= 2 , 0 <= @ <= pi/4 }

and 3/8 * pi ^2 answer in back of book is 3/64 * pi ^2


thankyou for your time!
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gabbagabbahey
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#2
Jan31-09, 02:26 AM
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Quote Quote by Andrew123 View Post
1. The problem statement, all variables and given/known data
ok change the region R = { (x,y) | 1 <= X^2 + y^2 <= 4 , 0 <= y <= x } to polar region and perform the double integral over region R of z=arctan(y/x)dA


2. Relevant equations
r^2 = x^2 + y^2, x = r*sin(@), y = r * cos (@)


3. The attempt at a solution

i got R = { (rcos(@), rsin(@) | 1 <= r <= 2 , 0 <= @ <= pi/4 }

and 3/8 * pi ^2 answer in back of book is 3/64 * pi ^2


thankyou for your time!
You've correctly converted to polar coordinates and found the limits of integration, but you somehow made a mistake evaluating the integral...Did you by chance forget that you are integrating the function [itex]\tan^{-1}\left(\frac{y}{x}\right)=\theta[/itex] over this region, andf just find the area of the region instead?
Andrew123
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#3
Jan31-09, 02:52 AM
P: 25
thankyou veeery much!

Mark44
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#4
Jan31-09, 10:37 AM
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xy coordinates to polar coordinates for double integral. hepl please!


Quote Quote by Andrew123;2056564[b
2. Relevant equations[/b]
r^2 = x^2 + y^2, x = r*sin(@), y = r * cos (@)
Not sure this made a difference in your answer, but the equations for x and y above are wrong. They should be
x = r*cos(theta)
y = r*sin(theta)


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