1. Find the volume under each surface and over the region bounded by the functions a) 2x + y + z = 6; x = 0; y = 0; z = 0, in the first octant b) z = 4-y²; x = 3; x = 0; y = 0; z = 0, in the first octant c) z = 1 + x² + y²; 3x + y = 3; x = 0; y = 0; z = 0, in the first octant

1. Find the volume under each surface and over the region bounded by the functions a) 2x + y + z = 6; x = 0; y = 0; z = 0, in the first octant b) z = 4-y²; x = 3; x = 0; y = 0; z = 0, in the first octant c) z = 1 + x² + y²; 3x + y = 3; x = 0; y = 0; z = 0, in the first octant

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

show full and complete procedure HANDWRITTEN only. Please answer a) b) and c) as they are subparts of one same question.

1.
Find the volume under each surface and over the region bounded by the functions
a) 2x + y + z = 6; x = 0; y = 0; z = 0, in the first octant
b)
z = 4-y²; x = 3; x = 0; y = 0; z = 0, in the first octant
c) z = 1 + x² + y²; 3x + y = 3; x = 0; y = 0; z = 0, in the first octant

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