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

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

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

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

3psilon
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.1Makes a bit of sense? :D Yay!
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