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1. Consider the region R in Quadrant II bounded by the line y = -x, the y-axis, and the circles, centered at the origin, of radius 3 and 4. (a) Sketch this region in the ry-plane, then sketch the corresponding region of the r,0-plane. Identify each boundary curve on one picture with a corresponding boundary curve on the other picture. (b) Recall that r and y depend on r and 0 according to the change of variable equations z = r cos(0) y =r sin(0) Calculate the matrix of partial derivatives, then find its determinant. Simplify your answer. dr dr dr d0 ду ду (c) Write the integral |/. arccos dA as an iterated integral in terms of r and 0.

1. Consider the region R in Quadrant II bounded by the line y = -x, the y-axis, and the circles, centered at the origin, of radius 3 and 4. (a) Sketch this region in the ry-plane, then sketch the corresponding region of the r,0-plane. Identify each boundary curve on one picture with a corresponding boundary curve on the other picture. (b) Recall that r and y depend on r and 0 according to the change of variable equations z = r cos(0) y =r sin(0) Calculate the matrix of partial derivatives, then find its determinant. Simplify your answer. dr dr dr d0 ду ду (c) Write the integral |/. arccos dA as an iterated integral in terms of r and 0.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.1: The Rectangular Coordinate System
Problem 40E: Find the exact volume of the solid that results when the region bounded in quadrant I by the axes...
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1. Consider the region R in Quadrant II bounded by the line y = -x, the y-axis, and the circles, centered at the origin, of radius 3 and 4. (a) Sketch this region in the ry-plane, then sketch the corresponding region of the r,0-plane. Identify each boundary curve on one picture with a corresponding boundary curve on the other picture. y (b) Recall that r and y depend on r and 0 according to the change of variable equations r =r cos(0) y = r sin(0) Calculate the matrix of partial derivatives, then find its determinant. Simplify your answer. dx dx ar 30 dy dy (c) Write the integral /, arccos dA as an iterated integral in terms of r and 0. + y?
Transcribed Image Text:1. Consider the region R in Quadrant II bounded by the line y = -x, the y-axis, and the circles, centered at the origin, of radius 3 and 4. (a) Sketch this region in the ry-plane, then sketch the corresponding region of the r,0-plane. Identify each boundary curve on one picture with a corresponding boundary curve on the other picture. y (b) Recall that r and y depend on r and 0 according to the change of variable equations r =r cos(0) y = r sin(0) Calculate the matrix of partial derivatives, then find its determinant. Simplify your answer. dx dx ar 30 dy dy (c) Write the integral /, arccos dA as an iterated integral in terms of r and 0. + y?
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