• anonymous
Hi all! Need serious Multivariable Calc help. Right now we're learning practical applications of double integrals: An annulus with inner radius r=1 and outer radius r=2 has density equal to delta(x,y)=3*(y+sqrt(x^2+y^2))/pi. Compute the mass of the annulus using polar coordinates. I get an answer, but I'm almost sure it's wrong.
MIT 18.02 Multivariable Calculus, Fall 2007
  • Stacey Warren - Expert
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  • katieb
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  • Vivek3461
The transformation from Rectangular/Cartesian coordinate to Polar coordinate is given by the substitution x=r.cos (theta) and y = r.sin (theta), where x,y are from cartesian coordinate and r, theta are from polar coornidate. r - Radial distance from centre ( range of is from 1 to 2 for this problem ) Theta - angle measured counter-clockwise wrt positive x-axis ( 0 to 2.pi for this problem) So to find the mass find the following, |dw:1391528427817:dw| V is the volume. But for the given problem the annular portion's thickness information is not given. So kindly cross check the problem statement. Or else assume unit thickness and proceed. :-)

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