The Theorem of Pappus states that when a plane region is revolved about a line which does not intersect the region except possibly at its boundaries, the volume of the solid formed is equal to the area of the region times the distance traveled by the centroid of the region. Use the Theorem of Pappus to set-up the integral that gives the volume of the solid formed when the triangle bounded by the y-axis, y = 5, and y = 2x + 1 is revolved about the y-axis.
The Theorem of Pappus states that when a plane region is revolved about a line which does not intersect the region except possibly at its boundaries, the volume of the solid formed is equal to the area of the region times the distance traveled by the centroid of the region. Use the Theorem of Pappus to set-up the integral that gives the volume of the solid formed when the triangle bounded by the y-axis, y = 5, and y = 2x + 1 is revolved about the y-axis.
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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Transcribed Image Text:The Theorem of Pappus states that when a plane region is revolved about a line which does not
intersect the region except possibly at its boundaries, the volume of the solid formed is equal to the area of
the region times the distance traveled by the centroid of the region. Use the Theorem of Pappus to set-up
the integral that gives the volume of the solid formed when the triangle bounded by the y-axis, y = 5, and
y = 2x + 1 is revolved about the y-axis.
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