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4 y = x(x-1)² Figure 1: Region from Question 3 (a) (a) Let R be the region bounded by the by the curve f(x) = x(x - 1)² and the z-axis (see Figure 1). Find the volume of the solid obtained by revolving R about the y-axis. (b) Let R be the region bounded by the curves y = ¹/3 and y = z in the first quadrant. Find the volume of the solid obtained by revolving R about the z-axis.

4 y = x(x-1)² Figure 1: Region from Question 3 (a) (a) Let R be the region bounded by the by the curve f(x) = x(x - 1)² and the z-axis (see Figure 1). Find the volume of the solid obtained by revolving R about the y-axis. (b) Let R be the region bounded by the curves y = ¹/3 and y = z in the first quadrant. Find the volume of the solid obtained by revolving R about the z-axis.

Advanced Engineering Mathematics
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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y = x(x - 1)² Figure 1: Region from Question 3 (a) X 3. (a) Let R be the region bounded by the by the curve f(x) = x(x − 1)² and the z-axis (see Figure 1). Find the volume of the solid obtained by revolving R about the y-axis. (b) Let R be the region bounded by the curves y = ¹/³ and y = x in the first quadrant. Find the volume of the solid obtained by revolving R about the z-axis.
Transcribed Image Text:y = x(x - 1)² Figure 1: Region from Question 3 (a) X 3. (a) Let R be the region bounded by the by the curve f(x) = x(x − 1)² and the z-axis (see Figure 1). Find the volume of the solid obtained by revolving R about the y-axis. (b) Let R be the region bounded by the curves y = ¹/³ and y = x in the first quadrant. Find the volume of the solid obtained by revolving R about the z-axis.
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