Calculating Volume of Region Revolved About y=4

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To calculate the volume of the region enclosed by the curves x=3y and x=-y^2+4 when revolved around y=4, both the shell and disc methods can be utilized. The shell method was established, while the disc method requires careful setup to ensure accuracy. The proposed disc method integral is pi integral(-4,1) ((3y-4)^2 - (-y^2)^2), but there are concerns about its correctness. Visualizing the region and the axis of rotation can aid in correctly setting up the integrals. Accurate representation of both methods is crucial for determining the volume effectively.
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Find the region enclosed by x=3y and x=-y^2+4. Set up integrals both shell and disc that represent the volume when this region is revolved about y=4.

i got the shell method, how would i represent the disc method>

pi integral(-4,1) (3y-4)^2-(-y^2)^2 --this is wat i got for disc method, though i am sure it is wrong...
 
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It might help you if you make a drawing -- draw the line that you're rotating about, and the region that is being rotated.
 

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