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anonymous
 one year ago
find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis
y =(x^2)+1 , y = 9  (x^2) about y = 1
anonymous
 one year ago
find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis y =(x^2)+1 , y = 9  (x^2) about y = 1

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freckles
 one year ago
Best ResponseYou've already chosen the best response.3I like a little visual. dw:1443749174250:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.3find the xcoordinates of the intersections there for the limit part

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\pi[\int\limits_{2}^{2}(10x^2)^2\int\limits_{2}^{2}(x^2+2)^2\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0this is what i have so far

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i think its wrong because i keep getting the wrong answer

freckles
 one year ago
Best ResponseYou've already chosen the best response.3dw:1443749494904:dw your radi look right

freckles
 one year ago
Best ResponseYou've already chosen the best response.3let me check your xcoordinates of your interesections

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[x^2+1=9x^2 \\ 2x^2=8 \\ x^2=4 \\ x= \pm 2\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.3what did you get as the answer after integration ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the final answer or do you want me to integrate it?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3give the answer and I will check it then if the answer is not what I have I might ask you to show me the integration

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i got 864pi for the final answer but wolframalpha says 256pi

freckles
 one year ago
Best ResponseYou've already chosen the best response.3ha so it is the integration

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[(10x^2)^2=10020x^2+x^4 \\ (2+x^2)^2=4+4x^2+x^4\] you get this for the expansion part?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3the difference would be ... \[9624x^2 \] \[\pi \int\limits_{2}^{2} (9624x^2) dx \\ \pi( 96x8x^3)_{2}^{2}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[i get 100x\frac{ 20x^3 }{ 3 }+\frac{ x^5 }{ 5 }\frac{ x^5 }{ 5 }\frac{ 4x^3 }{ 3 }+4x\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.3I think that one term should be 4x

freckles
 one year ago
Best ResponseYou've already chosen the best response.3but anyways you should be able to combine like terms after making that correct and get what I have above

freckles
 one year ago
Best ResponseYou've already chosen the best response.3it is fine what you did integrate then simplify I prefer to simplify then integrate most of the time

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[[100(2)\frac{ 20(2)^3 }{ 3 }\frac{ 4(2)^3 }{ 3 }4(2)][100(2)\frac{ 20(2)^3 }{ 3 }\frac{ 4(2) }{ 3 }4(2)]\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.3ick why not clean up before pluggin in numbers

freckles
 one year ago
Best ResponseYou've already chosen the best response.3if you prefer this, this is fine... but it looks gross to me :p

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0youre right but ive been working on this problem all day so im tryin to be explicit

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok i got it thank you

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[[200\frac{160}{3}\frac{32}{3}8][200+\frac{160}{3}+\frac{32}{3}+8] \\ (200+200)+(\frac{160}{3}\frac{160}{3})+(\frac{32}{3}\frac{32}{3})+(88) \\ (400)+(\frac{320}{3})+(\frac{64}{3})+(16) \\ \\ (40016)+(\frac{320}{3}+\frac{64}{3}) \\ (384)+(\frac{384}{3}) \\ 384(1\frac{1}{3}) \\ 384(\frac{2}{3}) \\ \frac{384}{3}(2) \\ (128)(2) \\ 256\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0my math was just a little off

freckles
 one year ago
Best ResponseYou've already chosen the best response.3is the way I would have continued from your last step there

freckles
 one year ago
Best ResponseYou've already chosen the best response.3and of course shove the pi in

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i got all the integration and the equation and messed up on the algebra

freckles
 one year ago
Best ResponseYou've already chosen the best response.3I think if you have simplified before integration would have made it tons easier

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0il keep that in mind these problems are taking longer and longer

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[\int\limits _{2}^{2}[(10x^2)^2(x^2+2)^2 ]dx\\ \int\limits_{2}^2 [(10020x^2+x^4)(x^4+4x^2+4)] dx \\ \int\limits_{2}^2 [(1004)+(20x^24x^2)+(x^4x^4)] dx \\ \int\limits_{2}^2 [9624x^2] dx \\ 96x24 \frac{x^3}{3} _{2}^2 \\ 96x8x^3_{2}^2 \\ (96 \cdot 2 8(2)^3)(96 \cdot (2)8(2)^3) \\ (19264)(192+64) \\(192+192)+(6464) \\ 384+(128) \\ 256\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.3just in case you wanted to see how I would tackled the integration and the after part
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