(a. (b. (c. (d. Consider the three dimensional solid E, that lies above the cone z = x²+ y²+z² = 32 with y > 0 and y > x x²+y2 and below the sphere Write down, but do not evaluate, the triple integral in cartesian coordinates that gives the volume of E. Include all limits of integration. Write down, but do not evaluate, the triple integral in cylindrical coordinates that gives the volume of E. Include all limits of integration. Write down, but do not evaluate, the triple integral in spherical coordinates that gives the volume of E. Include all limits of integration. Use the best suited integral from either (a.), (b.) or (c.) to determine the volume of E.
(a. (b. (c. (d. Consider the three dimensional solid E, that lies above the cone z = x²+ y²+z² = 32 with y > 0 and y > x x²+y2 and below the sphere Write down, but do not evaluate, the triple integral in cartesian coordinates that gives the volume of E. Include all limits of integration. Write down, but do not evaluate, the triple integral in cylindrical coordinates that gives the volume of E. Include all limits of integration. Write down, but do not evaluate, the triple integral in spherical coordinates that gives the volume of E. Include all limits of integration. Use the best suited integral from either (a.), (b.) or (c.) to determine the volume of E.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter8: Further Techniques And Applications Of Integration
Section8.2: Integration By Parts
Problem 29E
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