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.
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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Q3 (c) and (d) only please
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 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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