Consider the following. S S ST 6x² dv where T is the solid tetrahedron with vertices (0, 0, 0), (1, 0, 0), (0, 1, 0), and (0, 0, 1). (a) Describe the region D which is the projection of T over the xy-plane. (b) Describe the region T. (c) Evaluate the triple integral.

Consider the following. S S ST 6x² dv where T is the solid tetrahedron with vertices (0, 0, 0), (1, 0, 0), (0, 1, 0), and (0, 0, 1). (a) Describe the region D which is the projection of T over the xy-plane. (b) Describe the region T. (c) Evaluate the triple integral.

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 12E

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Question

Consider the following.
SS fr 6x² dv
where I' is the solid tetrahedron with vertices (0, 0, 0), (1, 0, 0), (0, 1, 0), and
(0, 0, 1).
(a) Describe the region D which is the projection of T over the xy-plane.
(b) Describe the region T.
(c) Evaluate the triple integral.

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Step 1: Analysis and Introduction

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Step 2: Describe the region D.

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Step 3: Describe the region T

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Step 4: Solve the integral

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