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anonymous
 4 years ago
**Calc2 Help** Surface Area generated by the curve y=x^3/2 from x = 0 to 3 about the xaxis.
anonymous
 4 years ago
**Calc2 Help** Surface Area generated by the curve y=x^3/2 from x = 0 to 3 about the xaxis.

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amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1so whats our integral look like?

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1\[2pi\int \sqrt{y^2(1+dy^2)}dx\]

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.132 = 1 3/2 x^1/2 is our derivative

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1\[2pi\int \sqrt{(x^{3/2})^2(1+(\frac{3}{2}x^{1/2})^2)}dx\] \[2pi\int_{0}^{3} \sqrt{x^3(1+\frac{9}{4}x)}dx\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0you can square the 4, so now it's just pi outside the integral.

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1is that:\[x^{3/2}\]or \[\frac{1}{2}x^3\]???

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1is it:\[y=x^{3/2}\] or \[y=\frac12 x^3\]???

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1let me fix up my int then :) \[2pi\int \sqrt{(\frac{x^{3}}{2})^2(1+(\frac{3}{2}x^{2})^2)}dx\] \[2pi\int_{0}^2 \sqrt{(\frac{x^{6}}{4})(1+(\frac{9}{4}x^{4}))}dx\] \[2pi\int_{0}^2 \sqrt{(\frac{x^{6}}{4})(\frac{4+9x^4}{4})}dx\] \[2pi\int_{0}^2 \sqrt{(\frac{4x^6+9x^{10}}{16})}dx\] \[\frac{pi}{2}\int_{0}^2 \sqrt{4x^6+9x^{10}}dx\]

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1doesnt really pretty up does it :)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ok so how did you bring the x^3/2 inside the sqrt??

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0haha all these things are freaking ugly!!

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1i undid it, for example \[\sqrt{a^2b}=a\sqrt{b}\]so to put it back in; square it

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.2why did you not finish prettying it amistre?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I tried it and got an ugly big number..

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1lol, cause this math latex is slowing my computer like mole asses

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.2lol\[\frac{\pi}2\int_{0}^{2}x^3\sqrt{4+9x^4}dx\]now it's beautiful!

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[2/3 * (4x^6 + 9x^(10))^(3/2)\]

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1still a bit yucky :) but im sure it trigs up nice http://www.wolframalpha.com/input/?i=integrate+%28pi%2F2%29%28sqrt%284x%5E6%2B9x%5E10%29%29+from+0+to+2

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1sqrt(tan^2) if im not mistaken

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0@amistre.. 52.1416 didn't work. :/

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1im not the expert at plugging into programs .... :)

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.2what trig?\[u=4+9x^4\to du=36x^3dx\]\[xdx=\frac{du}{72}\]\[\frac{\pi}{72}\int\sqrt udu\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0@Turing, that is what I had..

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.2let me see what I get

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I had pi/2 integral 2/3 * (9x^4 + 1 )^ (3/2)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0with limits 144 and..

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.2yeah I got 52.14... as well so I would have to read back and see what you guys were doing

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I HATE THIS STUFF!!!!!!!

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1does yout program say to round it to some deci spot?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.2hey wait, I integrated from 0 to 2, not 3 let me try again...

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.2577.041397813276 let me try to get a fraction...

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0it says 4 or 5 sig figs..

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1http://www.wolframalpha.com/input/?i=integrate+%282pi%29*%28x%5E3%2F2%29*%28sqrt%281%2B%283x%5E2%2F2%29%5E2%29%29+from+0+to+2 even without prettying it up and just plugging in the formula I get the same 52.

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.152.14164475991909058699913948569216045125036230794221370364473673799360642806811915388818213592188470 see if itll do that lol

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.2but the integral is from 0 to 3, no?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.052.14164475991909058699913948569216045125036230794221370364473673799360642806811915388818213592188470 HAHAHAHAHAAH.. THAT WORKED!!!

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Sorry for the caps, my excitement overtook my fingers.

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.2well it is obviously right, but the post says 0 to 3... I put in 0 to 2 at first as well, I must have picked up on it subconsciously

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0You guys are badass! Now it's time for me to study and to this crap on a test tomorrow morning.. Fun....

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Thank ya! Take care guys.. See you next week with a new set of problems.. This time they will not be solids of revolution, but spring related force.
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