- #1

meister

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**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.

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.