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 Calculus Calculus Math Forum

 November 10th, 2014, 10:02 AM #1 Newbie   Joined: Nov 2014 From: Texas Posts: 6 Thanks: 0 volume x-axis vs y-axis Hello again Math Forum community! I am already liking this bunch of people. So I am working on some volume problems and I am understanding most of context, but I am getting hung up on which formula to use for x vs y axis rotations. Example: "Find the volume of the region by revolving the region about the y-axis". The region enclosed by $\displaystyle x=y^\frac13, x=0, y=8$ A. $\displaystyle \frac{96}5\pi$ B. $\displaystyle 32\pi$ C. $\displaystyle 16\pi$ D. $\displaystyle 12\pi$ So which values do I use for the bounds of the integral? $\displaystyle \int_0^{y^\frac13}$????? And will the formula look like the following?: $\displaystyle \int_0^{y^\frac13}2\pi x {8}$ Do I have this backwards? November 10th, 2014, 11:21 AM #2 Senior Member   Joined: Mar 2011 From: Chicago, IL Posts: 214 Thanks: 77 Correct answer is A. Use the formula: Last edited by skaa; November 10th, 2014 at 11:23 AM. November 10th, 2014, 11:23 AM #3 Senior Member   Joined: Mar 2011 From: Chicago, IL Posts: 214 Thanks: 77 $\displaystyle V=\pi \int_{0}^{8}(y^{\frac{1}{3}})^2dy=\pi \int_{0}^{8}y^{\frac{2}{3}}dy=\frac{3}{5}\pi y^{\frac{5}{3}} |_0 ^8$ Thanks from thesheepdog Tags volume, xaxis, yaxis Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post thesheepdog Calculus 2 November 10th, 2014 09:21 AM Einstein Calculus 9 June 20th, 2014 11:05 AM r-soy Calculus 3 November 25th, 2012 12:31 PM spellbinder Calculus 1 June 2nd, 2011 11:22 PM Dontlookback Calculus 3 June 17th, 2010 09:11 AM

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