quiz_07D - Math 213 Quiz 7 Name Solution 1 Find the volume...

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Unformatted text preview: Math 213 -- Quiz 7 Name Solution 1. Find the volume of the solid in the first octant bounded by the cylinder z = 9 - y 2 and the plane x = 2. We are asked to find the volume below the graph of the function f (x, y) = 9 - y 2 above the rectangle R = [0, 2] [0, 3]. We choose to evaluate the following iterated integral 2 3 f (x, y) dA = R 0 0 9 - y 2 dy dx. For the inside integral, 3 9 - y 2 dy = 9y - 0 y3 3 3 = 18. y=0 For the outside integral, 2 18 dy = 36. 0 Therefore, the volume is 36. ...
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