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The double integral

The double integral

Calculus: Early Transcendentals
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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(a) The double integral II f(x, y) dA computes the volume of the solid over region D on the y-plane and below the surface z = f(x, y). The disk D = {(x, y)|x² + (y – 1)² < 1} may be described in polar (b) coordinates as - D = {(r,0)|0 < 0 < T,0 <r< 2 sin 0}.
Transcribed Image Text:(a) The double integral II f(x, y) dA computes the volume of the solid over region D on the y-plane and below the surface z = f(x, y). The disk D = {(x, y)|x² + (y – 1)² < 1} may be described in polar (b) coordinates as - D = {(r,0)|0 < 0 < T,0 <r< 2 sin 0}.
(d) use the following formula of spherical coordinates to compute the triple integral of f (x, y, z) over E: Suppose that E is a ball centered at (0,0,0) with radius 2. We can I| f(x, y, z)dV = | | | f(p,0, $)p² sin ødpdodø. E 0, 0, The point (x, y, z) = (-1, –1, –1) under rectangular coordinates in R³ (e) can be described through either cylindrical coordinates (r, 0, z) = ( v2, 4 or spherical coordinates (va (P, 0, $) = V3, -1 п — сOS 3
Transcribed Image Text:(d) use the following formula of spherical coordinates to compute the triple integral of f (x, y, z) over E: Suppose that E is a ball centered at (0,0,0) with radius 2. We can I| f(x, y, z)dV = | | | f(p,0, $)p² sin ødpdodø. E 0, 0, The point (x, y, z) = (-1, –1, –1) under rectangular coordinates in R³ (e) can be described through either cylindrical coordinates (r, 0, z) = ( v2, 4 or spherical coordinates (va (P, 0, $) = V3, -1 п — сOS 3
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