Consider the function f(x) = 4(4 + x^2)^-1/2 and the region R on the interval [0

Question

Consider the function f(x) = 4(4 + x^2)^-1/2 and the region R on the interval [0, 8/3]. See the figure to the right. Find the area of R Find the volume of the solid generated when R is revolved about the x-axis. Find the volume of the solid generated when R is revoked about the y-axis. Set up the integral that gives the volume of the solid generated when R is revolved about the x-axis Use increasing limits of integration. Select the correct choice below and fill in the answer boxes to your choice.

Explanation / Answer

Since , then   

(a)

(b) Volume, about :

If , then

If , then

             

(c) Volume, about axis:

                

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