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

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3psilon
 2 years ago
Best ResponseYou've already chosen the best response.0My answer differs from that of my teacher's. Can someone just show me the integral

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

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1Hmm 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.

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

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

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

3psilon
 2 years ago
Best ResponseYou've already chosen the best response.0It makes sense but can you explain why we subtract 3?

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1362721856820:dwThat new length is the outer radius.

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1If 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]\]

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

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1Bah I wish the drawing tool had more functionality :) lol

3psilon
 2 years ago
Best ResponseYou've already chosen the best response.0ohhhh 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!

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1Makes a bit of sense? :D Yay!
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