Let f (x, y, z) = (z^2 - x^2 - y^2) / (z^2 + x^2 + y^2) be the function of the image defined on the solid region D given by: -1 ≤ y ≤ 1 0 ≤ x ≤ √(1-y^2) 0 ≤ z ≤ x 1. The region of integration D, in cylindrical coordinates, is determined by 0≤ θ ≤π 0≤ r ≤1 0≤ z≤ rcosθ 2. The integral in cylindrical coordinates that describes the triple integral over D (first image)

Let f (x, y, z) = (z^2 - x^2 - y^2) / (z^2 + x^2 + y^2) be the function of the image defined on the solid region D given by: -1 ≤ y ≤ 1 0 ≤ x ≤ √(1-y^2) 0 ≤ z ≤ x 1. The region of integration D, in cylindrical coordinates, is determined by 0≤ θ ≤π 0≤ r ≤1 0≤ z≤ rcosθ 2. The integral in cylindrical coordinates that describes the triple integral over D (first image)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.5: Product-to-sum And Sum-to-product Formulas

Problem 4E

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Question

Let f (x, y, z) = (z^2 - x^2 - y^2) / (z^2 + x^2 + y^2) be the function of the image defined on the solid region D given by:
-1 ≤ y ≤ 1
0 ≤ x ≤ √(1-y^2)
0 ≤ z ≤ x

1. The region of integration D, in cylindrical coordinates, is determined by
0≤ θ ≤π
0≤ r ≤1
0≤ z≤ rcosθ

2. The integral in cylindrical coordinates that describes the triple integral over D (first image)

Which is correct or which is incorrect?

•7/2
r cos e ,2 - p2
rdzdrde
-T/2 Jo
z2 + r2

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

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