Question

Consider the plane region R bounded by the curve y = x − x 2 and...

Consider the plane region R bounded by the curve y = x − x 2 and the x-axis. Set up, but do not evaluate, an integral to find the volume of the solid generated by rotating R about the line x = −1

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Answer #1

we can plot the given region as follows,

Consider a shell at a distance x from the y-axis.

Then the distance b/w the shell and axis of rotation is the radius of rotation given by,

The height of the shell is given by,

The volume of rotation about the vertical line using the shell method is given by,

plugin the values,

plugin the limits,

I hope this answer helps,
Thanks,
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