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anonymous
 one year ago
Which integral correctly computes the volume formed when the region bounded by the curves x2 + y2 = 25, x = 3 and y = 0 is rotated around the yaxis?
HELP PLEASE
anonymous
 one year ago
Which integral correctly computes the volume formed when the region bounded by the curves x2 + y2 = 25, x = 3 and y = 0 is rotated around the yaxis? HELP PLEASE

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jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1Have you sketched it out for yourself? I'm beginning to sketch it for myself right now.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1From what I'm getting the bounded area is sort of like a pie slice, and the volume looks like a doughnut or something. It's got a big hole through the center.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1dw:1438138779545:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i know the intefral has sqrt 25y^2 in it

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1Yes, that's a good start. We need to take into account the hole as well in order to get the correct integral.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1Our slices are basically "washers" or cylinders with holes. From above, the slices look like this:

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1dw:1438138974699:dw

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1The area of interest is given by taking the big circle area minus the small circle area: \[\pi(\sqrt{25y^2})^2  \pi(3)^2\] This gives us \[\pi(14  y^2)\] when simplified.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1Now for the fun part. Integrating that expression! :)

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1We need to integrate from y = 0 to y = 4... do you want to know how I got the y = 4 or did you figure that out?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i just needed to know what the integral would be :p

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1Doing the integration for these problems is sort of the "easy" part right? Imagining and drawing them takes patience and practice. :)

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1Let me know if you get stuck anywhere on the problem. Good luck!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0drawing it is where I have the most difficulty but you were much help

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1Yep, just keep practicing and trying to draw things. Look up problems with answers online and just practice the drawing part. Don't even integrate. That might be the best way to master these types of problems. :)
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