Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the specified axis. y=4x-x^2 y=3 about x=1

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Step-by-step explanation:

I graphed the region in the image below. The blue line is y=3, the purple line is x=1 and the green curve is y = . The shaded region in blue is the region we are going to rotate.

Now, to find the volume  v= where a=1, b=3 (left and right points of the region), p(x) is the distance from the rotation axis to the diferential Δx, we say p(x)=x and h(x) is the height of the region, in this case is h(x)= . Then,

v =  

=  

=

=

=

=  .

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step-by-step explanation: