Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Q3 (e) and (f) only please. Thanks! 

3. Let R be the region bounded by the lines ax = 0, y= 3x and y = 10- x. (a) Sketch the region R. Label the curves, their intersection points and lightly shade the region. (b) Calculate the area of the region using (i) an x-integral and (ii) a y-integral. (c) The base of a solid is R, and the cross-sections perpendicular to the x-axis are isosce- les right triangles with height on the base. Set-up an expression with integrals that calculates the volume of the solid. (d) The base of a solid is R, and the cross-sections perpendicular to the y-axis are semicircles with diameter in the base. Set-up an expression with integrals that calculates the volume of the solid. = (e) We create a solid of revolution by revolving R about the line y 12. Set up an expression with integrals that calculates the volume of the solid using the washer method (f) We create a solid of revolution by revolving R about the line x = -2. Set up an expression with integrals that calculates the volume of the solid using the washer method. î
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Transcribed Image Text:3. Let R be the region bounded by the lines ax = 0, y= 3x and y = 10- x. (a) Sketch the region R. Label the curves, their intersection points and lightly shade the region. (b) Calculate the area of the region using (i) an x-integral and (ii) a y-integral. (c) The base of a solid is R, and the cross-sections perpendicular to the x-axis are isosce- les right triangles with height on the base. Set-up an expression with integrals that calculates the volume of the solid. (d) The base of a solid is R, and the cross-sections perpendicular to the y-axis are semicircles with diameter in the base. Set-up an expression with integrals that calculates the volume of the solid. = (e) We create a solid of revolution by revolving R about the line y 12. Set up an expression with integrals that calculates the volume of the solid using the washer method (f) We create a solid of revolution by revolving R about the line x = -2. Set up an expression with integrals that calculates the volume of the solid using the washer method. î
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Step 1: Define the problem
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Step 2: Draw the region R
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Step 3: Draw the figure of solid when region R rotated about line y=12
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Step 4: Calculate the set up of the integral for volume
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Step 5: Draw the graph of solid when region R rotated about line x=-2
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Step 6: Calculate the set up of the integral for volume
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Step 7: Continuation above step
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Solution
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