Volumes, applications of integrations

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To find the volume of the solid formed by rotating the region bounded by the curves y=x^4 and y=1 about the line y=2, the problem can be set up using either the disk or shell method. The key is to determine the area of the cross-sections perpendicular to the axis of rotation. Clarification is needed on whether to apply Pappus's centroid theorem or stick with traditional methods. Understanding the distinction between finding area versus volume is crucial for solving the problem effectively. Proper setup will lead to the correct volume calculation.
afcwestwarrior
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find the volume of the solid by rotating the region bounded by the given curves about the specified line,

y=x^4, y=1; about y=2

how do i set up the problem so i can figure out the area, i don't need the answer, and i already graphed it, and i already rotated the graph,
 
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Why do you want to find the area since you were asked for volume? Do you want to use a theorem of Pappus? Or would you rather use shells or disks? I don't exactly get the question.
 
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