Question

User polar coordinates to evaluate the integral.

double integral of (x^2) / (x^2+y^2)

R is bounded by x^2+y^2=a^2 and x^2+y^2=b^2
0 < a < b

Answer 1

how do you think we should start off this problem?

Answer 2

i have absolutely no freaking idea LOL

Answer 3

well you remeber those formulas right?

x=rcos(theta)

y=rsin(theta)

x^2+y2=r^2

Answer 4

so start by converting the function your are given to integrate into polar form, by replacing the x^2 with r^2cos^2(theta) and so on..

Answer 5

i'm guessing convert fx into polars so r^2cos^2(theta) / r^2

Answer 6

i'm assuming my theta region is 0 to theta, but i'm not quite sure what to do with r.. what's an annular region? lol

Answer 7

a, b

Answer 8

or it it should be the area lying between both circles

Answer 9

so the limits for r should be from a to b and the limits for theat should be from 0 to 2pi

Answer 10

Perhaps ...
\[ \int_{0}^{2\pi}\int_{a}^{b} \cos^2 \theta\; r\;drd\theta\]