I'm currently taking multivariable calculus and we're studying double and triple integration. The actual integration itself is easy, but what I am not understanding at all is how to find the intervals for integration. I can only manage to find them on only the most simple problems. I don't need help solving the integral, just help finding the limits of integration. At least I hope I'm doing the integration correctly...(adsbygoogle = window.adsbygoogle || []).push({});

Example 1

Find the volume of the solid bounded by the cylinder x^2+z^2=9 and the planes x=0, y=0, z=0, x+2y=2 in the first octant.

For this problem, all variables must be positive, so, 0<=x<=3 and 0<=y<=1-x/2. This doesn't appear to yield the correct answer however...On this one I integrated [squ](9-x^2). Is that the correct function to integrate? The right answer for this one is (1/6)(11[squ]5-27)+(9/2)arcsin(2/3). I get something relatively close but ultimately incorrect.

Example 2

Use a double integral to find the area of the region enclosed by the lemniscate r^2=4cos(2theta).

On this I assumed the interval of r would be from 0 to when cos(2theta) was 1, so 0<=r<=4 and 0<=theta<=2pi. This doesn't yield the correct answer either, however. The right answer on this one is 4, I get 0.

Any help at all is greatly appreciated. Note that I don't need you to solve the problems for me, just help me understand how to compute the intervals. Thanks.

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# Double integration Intervals

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