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Tutorial Exercise Use a double integral in polar coordinates to find the volume V of the solid bounded by the graphs of the equations. z = In(x2 + y²) z = 0 x2 + y2 > 4 x² + y? < 16 Step 1 Recall that the volume of a solid in any region R is given by JJ, f(x, y)dydx. R Here, f(x, y) = z = In(x2 + y?). To write the iterated integral in polar coordinates, recall that the polar coordinates (r, 0) of a point are related to the rectangular coordinates (x, y) by the following. X = r cos 0 y = r sin 0 Also, recall that x² + y? dy dx = dr d0 Submit Skip (you cannot come back)

Tutorial Exercise Use a double integral in polar coordinates to find the volume V of the solid bounded by the graphs of the equations. z = In(x2 + y²) z = 0 x2 + y2 > 4 x² + y? < 16 Step 1 Recall that the volume of a solid in any region R is given by JJ, f(x, y)dydx. R Here, f(x, y) = z = In(x2 + y?). To write the iterated integral in polar coordinates, recall that the polar coordinates (r, 0) of a point are related to the rectangular coordinates (x, y) by the following. X = r cos 0 y = r sin 0 Also, recall that x² + y? dy dx = dr d0 Submit Skip (you cannot come back)

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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Tutorial Exercise Use a double integral in polar coordinates to find the volume V of the solid bounded by the graphs of the equations. In(x? + y?) z = z = 0 x2 + y2 > 4 x2 + y2 < 16 Step 1 Recall that the volume of a solid in any region R is given by JJ, F(x, y)dydx. Here, f(x, y) = z = In(x2 + y?). To write the iterated integral in polar coordinates, recall that the polar coordinates (r, 0) of a point are related to the rectangular coordinates (x, y) by the following. X = r cos 0 y = r sin 0 Also, recall that x2 + y2 %3D dy dx dr de %D Submit Skip (you cannot come back),
Transcribed Image Text:Tutorial Exercise Use a double integral in polar coordinates to find the volume V of the solid bounded by the graphs of the equations. In(x? + y?) z = z = 0 x2 + y2 > 4 x2 + y2 < 16 Step 1 Recall that the volume of a solid in any region R is given by JJ, F(x, y)dydx. Here, f(x, y) = z = In(x2 + y?). To write the iterated integral in polar coordinates, recall that the polar coordinates (r, 0) of a point are related to the rectangular coordinates (x, y) by the following. X = r cos 0 y = r sin 0 Also, recall that x2 + y2 %3D dy dx dr de %D Submit Skip (you cannot come back),
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