Let R be the region bounded by the curves y=x^2, y=sin(xpi/2), x=0, and x=1. Find the volume of the solid obtained by rotating R around the y-axis.
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Note that: A graph of this would be helpful in visualizing what's going on. By method of shells: x = the radius of the shell; = represents the height of te shell
how would i solve that integral? it looks complicated
It's not too bad: You can integrate term by term (since: ) in which case the 2nd term should be rather easy. The first one, i.e. requires integration by parts: Sub it into the integration by parts formula and you should be on your way.
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