Determine volume of the solid of revolution formed by rotating about the x-axis the region bounded by the given curves.
, , ,
In order to solve this problem, remember the following.
If is non-negative and R is the region between and the x-axis from to , then the volume of the solid formed by rotating R about the x-axis is given by
Graphing the given equations will help us set up an appropriate definite integral for finding the desired volume.
Equations and each yield a graph of a vertical line.
Equation corresponds to the x-axis.
Function yields the graph of a line with slope 1 and y-intercept
From the graph see that is non-negative on the region R
Rotating R about the x-axis yields the solid
Using and, the volume of the desired solid is given by the definite integral
Applying the Fundamental Theorem of Calculus yields
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