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1) Use a double integral to find the area of the region enclosed by y= x² and y = 2x.

1) Use a double integral to find the area of the region enclosed by y= x² and y = 2x.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.5: Polar Coordinates
Problem 98E
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1) Use a double integral to find the area of the region enclosed by y= ÷x² and y = 2x. 2) Use polar coordinates to evaluate ff, sin OdA with R being the region in the first quadrant outside the circle r= 2 and inside the cardioid r= 2 + 2 cos 0. 3) Find the surface area of the portion of the paraboloid z = x² + y2 below the plane z = 1. 4) Use rectangular coordinates and a triple integral to fine the volume of the solid region enclosed by z = 5x2 + 5y? and z = 6 – 7x² – y². V9-x2 c9-x2-y² 5) Use cylindrical coordinates to evaluate , S x²dzdydx. 6) Use spherical coordinates to evaluate S, Sz SN 4-x2 4-x2-y2 z2. + y2 + z²dzdydx. x2
Transcribed Image Text:1) Use a double integral to find the area of the region enclosed by y= ÷x² and y = 2x. 2) Use polar coordinates to evaluate ff, sin OdA with R being the region in the first quadrant outside the circle r= 2 and inside the cardioid r= 2 + 2 cos 0. 3) Find the surface area of the portion of the paraboloid z = x² + y2 below the plane z = 1. 4) Use rectangular coordinates and a triple integral to fine the volume of the solid region enclosed by z = 5x2 + 5y? and z = 6 – 7x² – y². V9-x2 c9-x2-y² 5) Use cylindrical coordinates to evaluate , S x²dzdydx. 6) Use spherical coordinates to evaluate S, Sz SN 4-x2 4-x2-y2 z2. + y2 + z²dzdydx. x2
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