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# Calculus - volume

I have a couple of problems I need assistance with. Please include complete explanation and work. (see attached for equations)

Question 3: Consider the region R bounded by the curves y = 0, y = x-2, and y = .
a). Sketch the region R.

b). Set up (do not evaluate) the integral for computing the volume of the solid generated by revolving R about the

x -axis
y-axis

b) Evaluate the second integral.

Question 5: Find the volume of the solid generated by revolving the region bounded by the graphs of the equations

#### Solution Preview

(3) the curves y = sqrt(x), and y = x - 2 intersect at (0, 0) and (4, 2);

the volume got by revolving the region bounded by these curves and y=0 about the y-axis (using the disc method) is

pi. Int{0 to 2} [(y + 2)^2 - (y^2)^2 ] dy

since y = x - 2 ==> x = y + 2 and y = sqrt(x) ==> x = y^2 , and y runs from 0 to 2 (along the y-axis)
as x runs from 0 to 4.

Evaluating the integral ...

#### Solution Summary

This provides examples of finding volume of a solid using calculus.

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