by sfdsdga on July 31st, 2009

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Compute the volume of the solid formed by revolving the fourth quadrant region bounded by y = x2 - 1 , y = 0, and x = 0 about the line y = 2. a. 43p/15 b. 203p/15 c. 328p/15 d. 668p/15 e. 36p/5 f. 161p/5 g. 176p/3 h. none of these

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by Doug138 on August 1st, 2009
Integrate the function (x^2 - 1) - the function y = 0. Of course the subtract part is irrelevent, but it's still part of the process.

Then evaluate from -1 to 0, which is the part that exists in QIV. Basically you evaluate 1/3x^3 - x at x=-1. That is the area of the 2D part.

Rotating that about y=2 means your radius is 2.
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- There are several correct ways to do this. I would rotate the solid (all the way to the center at y=2) and then subtract out the perfect cylinder (length 1, radius 2) inside it.
  
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  by Doug138 on August 1st, 2009
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Compute the volume of the solid formed by revolving the fourth quadrant region bounded by y = x2 - 1 , y = 0, and x = 0 about the line y = 2. a. 43p/15 b. 203p/15 c. 328p/15 d. 668p/15 e. 36p/5 f. 161p/5 g. 176p/3 h. none of these

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Compute the volume of the solid formed by revolving the fourth quadrant region bounded by y = x2 - 1 , y = 0, and x = 0 about the line y = 2. a. 43p/15 b. 203p/15 c. 328p/15 d. 668p/15 e. 36p/5 f. 161p/5 g. 176p/3 h. none of these

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