2. Use a spherical coordinate system (p, p, 0) to find the volume between the sphere x? + y² + z? = 4 and the upper cone z = Зx2 + Зу?. (a) Draw a 3-D diagram and a convenient 2-D projection in the...



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2. Use a spherical coordinate system (p, p, 0) to find the volume between<br>the sphere x? + y² + z? = 4 and the upper cone z =<br>Зx2 + Зу?.<br>(a) Draw a 3-D diagram and a convenient 2-D projection in the yz-plane.<br>(b) Use the information above to determine the limits of integration.<br>(c) Set up the iterated triple integral and evaluate it to determine the volume.<br>(d) What would be the limits if we were restricted in the first octant only?<br>

Extracted text: 2. Use a spherical coordinate system (p, p, 0) to find the volume between the sphere x? + y² + z? = 4 and the upper cone z = Зx2 + Зу?. (a) Draw a 3-D diagram and a convenient 2-D projection in the yz-plane. (b) Use the information above to determine the limits of integration. (c) Set up the iterated triple integral and evaluate it to determine the volume. (d) What would be the limits if we were restricted in the first octant only?

Jun 04, 2022
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