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(16) Use a double integral to find the area of the region enclosed by both of the cardiods r=1+ cos 0 and r= 1- cos e.

(16) Use a double integral to find the area of the region enclosed by both of the cardiods r=1+ cos 0 and r= 1- cos e.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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TUTORIAL 6: 15.2 AND 15.3 Section - 15.2 (10) Evaluate the double integral. ff y/x-y dA, D = {(x,y)| 0< x < 2, 0 <y<x}. (14) Express D as a region of type I and also as a region of type II. Then evaluate the double integral in two ways. JJ xy dA, D is enclosed by the curves y x, y 3x. D (16) Set up iterated integrals for both orders of integration. Then evaluate the double integral using the easier order and explain why it's easier. f y?exy dA, D is bounded by the lines y = x, y = 4, x = 0. (22) Evaluate the double integral. ff ydA, D is the triangular region with vertices (0,0), (1,1), and (4,0). (29) Find the volume of the given solid bounded by the coordinate planes and the plane 3x + 2y + z = 6. (50) Sketch the region of integration and change the order of integration. o Src tan x (x, y) dy dx. Section 15.3 (16) Use a double integral to find the area of the region enclosed by both of the cardiods r = 1+ cos 0 and r= 1- cos 0. (26) Use polar coordinates to find the volume of the solid bounded by the paraboloids z=6- x-- y- and z (32) Evaluate the iterated integral by converting to polar coordinates. ydx dy. 2.x2 + 2y?. ENG 202 DE Ges 99+ 立
Transcribed Image Text:TUTORIAL 6: 15.2 AND 15.3 Section - 15.2 (10) Evaluate the double integral. ff y/x-y dA, D = {(x,y)| 0< x < 2, 0 <y<x}. (14) Express D as a region of type I and also as a region of type II. Then evaluate the double integral in two ways. JJ xy dA, D is enclosed by the curves y x, y 3x. D (16) Set up iterated integrals for both orders of integration. Then evaluate the double integral using the easier order and explain why it's easier. f y?exy dA, D is bounded by the lines y = x, y = 4, x = 0. (22) Evaluate the double integral. ff ydA, D is the triangular region with vertices (0,0), (1,1), and (4,0). (29) Find the volume of the given solid bounded by the coordinate planes and the plane 3x + 2y + z = 6. (50) Sketch the region of integration and change the order of integration. o Src tan x (x, y) dy dx. Section 15.3 (16) Use a double integral to find the area of the region enclosed by both of the cardiods r = 1+ cos 0 and r= 1- cos 0. (26) Use polar coordinates to find the volume of the solid bounded by the paraboloids z=6- x-- y- and z (32) Evaluate the iterated integral by converting to polar coordinates. ydx dy. 2.x2 + 2y?. ENG 202 DE Ges 99+ 立
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