et V be the region below the plane z = 4, outside the sphere x ^ 2 + y ^ 2 + z ^ 2 = 4 and inside the semicon (img9). When raising the integral: I = ∭Tf (x, y, z) dV in the spherical coordinates x = rcos (θ) sin (ϕ), y = rsin (θ) sin (ϕ), z = rcos (ϕ) we obtain: (img10)

et V be the region below the plane z = 4, outside the sphere x ^ 2 + y ^ 2 + z ^ 2 = 4 and inside the semicon (img9). When raising the integral: I = ∭Tf (x, y, z) dV in the spherical coordinates x = rcos (θ) sin (ϕ), y = rsin (θ) sin (ϕ), z = rcos (ϕ) we obtain: (img10)

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

Let V be the region below the plane z = 4, outside the sphere x ^ 2 + y ^ 2 + z ^ 2 = 4 and inside the semicon (img9). When raising the integral:

I = ∭_Tf (x, y, z) dV

in the spherical coordinates x = rcos (θ) sin (ϕ), y = rsin (θ) sin (ϕ), z = rcos (ϕ) we obtain:
(img10)

4 sec(4)
I I"F(r,0, 4)r² sin(4)drdød®
T/3
4 sin(4)
f(r, 0, $)r² sec(0)drdðdø
4 sec(4)
f(r,0, $)drd0dø
•7/3
27
27
•T/3
4 sin(4)
LI1"f(r, 0, $)r sec² (0)d0drdø
4
4 sec(4)
f(r,0, $)r sin(4)drdðdø
T/3

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