1. The problem statement, all variables and given/known data 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 2. Relevant equations mass of plate equation= double integral u(x,y) dx dy 3. 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!