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Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y-axis.

$ y = 4x - x^2 $ , $ y = x $

$\frac{27 \pi}{2}$

Applications of Integration

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In order to use the method of cylindrical shells, we first know that we need to find the intersections. So if access that equal to four x minus x squared solved and we end up with acts Times X minus three is you remember we're trying to solve for acts forgetting intersection points because thes are actually gonna be our bounce. Now remember the general formula for volume as two pi times into girl from A to B, which is the earthly We just figured that out with our intersection points are age, times D backs greatest times Hey, essentially OK, plug in Everything we know are times h. Now we know that with me integrate, we're gonna be using the powerful, which means increased the exponent by one divide by the new Acciona. Okay, Now we know we're gonna be plugging n when we plug in zero. We actually just end up with zero Simple five. We end up with 27 pi divided by two