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3. Let R be the region bounded by the lines x = 0, y = VT 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.

3. Let R be the region bounded by the lines x = 0, y = VT 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.

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 41E: Find the exact lateral area of each solid in Exercise 40. Find the exact volume of the solid formed...
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Q3. From b onwards please
3. Let R be the region bounded by the lines x = 0, y = x 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 had 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.
Transcribed Image Text:3. Let R be the region bounded by the lines x = 0, y = x 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 had 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.
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