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Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the curves y=2+x−x^2 and y+x=2 about the y-axis. Below is a graph of the bounded region.

Question

Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the curves y=2+x−x^2 and y+x=2 about the y-axis. Below is a graph of the bounded region.

check_circleAnswer
Step 1

The formula to calculate the volume using ...

h
V =[27x[f(x) ]ds
a
Compute the value ofx as follows.
2 x-x x+2
-x2 2x 0
x2-2x 0
x(x-2) 0
x-0,x 2
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h V =[27x[f(x) ]ds a Compute the value ofx as follows. 2 x-x x+2 -x2 2x 0 x2-2x 0 x(x-2) 0 x-0,x 2

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Calculus

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