Calculus Calculus Math Forum

March 26th, 2019, 06:52 AM   #1
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Multivariable calculus

I am unable to set the limits and reach the conclusive answer and mark the correct option. I am trying to put the the solution in cylindrical coordinates but the answer I am getting is not matching with the options. Please help with the answer and more important the steps to reach such a rigorous conclusion. Attached Images 20190326_182627.jpg (94.3 KB, 9 views) March 26th, 2019, 10:55 AM #2 Senior Member   Joined: Sep 2015 From: USA Posts: 2,636 Thanks: 1472 $F=(y^2, 2xy,xz^2)$ $S = (x, y, x^2 + y^2)$ $S_x = (1,0,2x)$ $S_y = (0,1,2y)$ $dS = S_x \times S_y = (-2x,-2y,1)$ $\nabla \times F = (0,-z^2, 0)$ $\nabla \times F \cdot dS = 2yz^2$ To do the integration we convert to cylindrical coordinates. $\nabla \times F \cdot dS =2r \sin(\theta) r^4 = 2r^5 \sin(\theta)$ $\displaystyle \int_0^{\frac \pi 2}\int_0^1 2r^5 \sin(\theta)~r ~dr~d\theta = \dfrac 2 7$ Thanks from topsquark and shashank dwivedi Tags calculus, multivariable 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 cargar Calculus 3 March 21st, 2019 12:54 PM akansel Calculus 6 October 16th, 2017 09:44 AM maluita659 Calculus 7 February 15th, 2014 02:15 PM summerleei Real Analysis 1 December 5th, 2013 06:49 AM Ecomat Math Books 1 July 2nd, 2012 04:07 AM

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