?The following problems concern the Theorem of Pappus (see Moments and Centers of Mass
Chapter 5, Problem 442(choose chapter or problem)
The following problems concern the Theorem of Pappus (see Moments and Centers of Mass (http://cnx.org/ content/m53649/latest/) for a refresher), a method for calculating volume using centroids. Assuming a region R, when you revolve around the x-axis the volume is given by \(V_{x}=2 \pi A \bar{y}\) , and when you revolve around the y-axis the volume is given by \(V_{y}=2 \pi A \bar{x}\) , where A is the area of R. Consider the region bounded by \(x^{2}+y^{2}=1\) and above y = x + 1.
Find the volume when you revolve the region around the y-axis.
Text Transcription:
V_x = 2 pi A bar y
V_y = 2 pi A bar x
x^2 + y^2 = 1
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