Tuesday, October 16, 2018

12.3 #8


Hello,

Would you be able to help me understand why my bounds are wrong? I listed by bounds as a = 3pi/2, b = pi/2, c = 1, and d = 3 as integral set up from a to b, integral c to d (frdrdt).

Thank you,





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Well, there are a couple ways you got tangled up.  First of all, your outer limits of integration refer to the angular variable on the negative and positive y-axis while your inner variable is θ, so that you either need to have θ on the outside or make c,d refer to the angular variable.  Second, you have a bigger than b. That means when you do an integral that you are doing integral backwards, so that integral would be over the opposite half washer--the one with the negative x-values.  I recommend that you use -π/2 to π/2 instead.