2 questions: find the volume

Limits, differentiation, related rates, integration, trig integrals, etc.

2 questions: find the volume

Postby junsta12 on Sun Mar 02, 2014 6:00 pm

1) find the volume obtained by rotating the region bounded by x=0 and x=y-y^2 about the y-axis.

-I was able to use the disc method and come up with the formula: Pi*(1/2*y^2-1/3*y^3) but i do not know where to go from here. finding the intervals would be my guess but i don't know how.

2)find the volume obtained by rotating the region bounded by the x-axis, y=1/x, x=1, and x=2 about the line y=1.

-I am completely lost on this.
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Re: 2 questions: find the volume

Postby nona.m.nona on Tue Mar 04, 2014 1:03 am

junsta12 wrote:1) find the volume obtained by rotating the region bounded by x=0 and x=y-y^2 about the y-axis.

-I was able to use the disc method and come up with the formula: Pi*(1/2*y^2-1/3*y^3) but i do not know where to go from here. finding the intervals would be my guess but i don't know how.

By "formula", do you mean "result, upon integration"? By "intervals", do you mean "limits of integration"?

junsta12 wrote:2)find the volume obtained by rotating the region bounded by the x-axis, y=1/x, x=1, and x=2 about the line y=1.

-I am completely lost on this.

One might begin by graphing the region, as outlined in the exercise statement. Upon completion, one might then determine the integrand, given the stated limits of integration.
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