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Let C denote the solid that is = 0, • bounded above by z = e-2(x² +y² ), and • lying within the cylinder x? + y² • bounded below by z = 4. We want to calculate the volume of the solid, which is given by the triple integral dV.

Let C denote the solid that is = 0, • bounded above by z = e-2(x² +y² ), and • lying within the cylinder x? + y² • bounded below by z = 4. We want to calculate the volume of the solid, which is given by the triple integral dV.

Calculus For The Life Sciences
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
Section8.3: Volume And Average Value
Problem 1E
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Let C denote the solid that is = 0, - 2 (x² + y² ), • bounded below by z = • bounded above by z = e and lying within the cylinder x + y² = 4. We want to calculate the volume of the solid, which is given by the triple integral dV. (a) In cylindrical coordinates, the bounds of integration for 0, r, and z are given by <r < < z < (b) What is the volume of the solid C? (If you enter your answer using a decimal approximation, then round your answer to three decimal places.) Volume(C) :
Transcribed Image Text:Let C denote the solid that is = 0, - 2 (x² + y² ), • bounded below by z = • bounded above by z = e and lying within the cylinder x + y² = 4. We want to calculate the volume of the solid, which is given by the triple integral dV. (a) In cylindrical coordinates, the bounds of integration for 0, r, and z are given by <r < < z < (b) What is the volume of the solid C? (If you enter your answer using a decimal approximation, then round your answer to three decimal places.) Volume(C) :
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