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jamesdocherty
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Homework Statement
Let the path C traverse part of the circle or radius 3 at the origin, in a clockwise direction, from (0,-3) to (3,0). Calculate the total mass of a wire in shape C, if the mass density of the wire is u=x^2+4y
Homework Equations
mass of plate equation= double integral u(x,y) dx dy
The Attempt at a Solution
I converted the wire into polar coordinates as its a circle, with x=3cos(theta) and y=3sin(theta) and as it travels from -pi/2 to 2pi, 0<r<3 and -pi/2<theta<2pi, after doing that i subbed x=3cos(theta) and y=3sin(theta) into the mass density equation (u) to obtain u=9cos^2(theta) + 12sin(theta) and as the mass of plate equation is double integral u(x,y) dx dy I subbed the vaules into this equation but with respect to polar coordinates to get:
double integral 9cos^2(theta) + 12sin(theta) dtheta dr with 0<r<3 and -pi/2<theta<2pi
solving this ended up getting 135*pi/4 -36 to be the answer, but I'm a little confused as i think i worked out the mass for 3/4 of the circle, instead of the wire and am now thinking i might need to work out a ratio for area of circumference/total area of circle and multiply by this ratio to get the right answer.
Any Help would be much appreciated!