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rotate the region bounded by y = 6  2x  x^2 and y = x+6 about the line y=3
 one year ago
 one year ago
rotate the region bounded by y = 6  2x  x^2 and y = x+6 about the line y=3
 one year ago
 one year ago

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3psilonBest ResponseYou've already chosen the best response.0
My answer differs from that of my teacher's. Can someone just show me the integral
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Can you provide the teacher's answer a sec? I wanna see if I made some terrible mistake before I post this integral :P
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Hmm this is setup really strangly... Clearly the parabola is our upper function. So why is the parabola being subtracted from the line... This is what I came up with, \[\large \pi \int\limits_{3}^0 \left[(62xx^2)3\right]^2\left[(x+6)3\right]^2\;dx\] I should look over my work again though.. bit of a tricky problem. I may have made a mistake somewhere.
 one year ago

3psilonBest ResponseYou've already chosen the best response.0
But I thought the outer radius was at a height 3 plus the parabola function so why wouldn't it be 3+(62xx^2)?
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
dw:1362721421835:dwSo the outer radius \(\large R\) is going to be \(\large y_13\). Where \(\large y_1=62xx^2\).
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
I hope that drawing makes sense... :\ I took a slice and spun it around y=3. And drew some lines to figure out the radius.
 one year ago

3psilonBest ResponseYou've already chosen the best response.0
It makes sense but can you explain why we subtract 3?
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
dw:1362721856820:dwThat new length is the outer radius.
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
If we were to draw a disk (not hollowed out) with that radius, it would look like this.dw:1362722006047:dw This area of this disk, minus the area of, dw:1362722103066:dw Gives us the area of our disk hollowed out,\dw:1362722226356:dw[\large A=\pi\left[R^2r^2\right]\]
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
\[\large A=\pi\left[R^2r^2\right]\]
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Bah I wish the drawing tool had more functionality :) lol
 one year ago

3psilonBest ResponseYou've already chosen the best response.0
ohhhh okay okay ! I always had trouble seeing that part! Thank you ! hhha I really appreciate the drawings they helped a lot! Thanks for helping me get ready for my test!
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Makes a bit of sense? :D Yay!
 one year ago
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