My Math Forum ONE OF MANY ERRORS IN CALCULUS-2

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 December 18th, 2012, 12:21 PM #1 Newbie   Joined: Dec 2010 Posts: 17 Thanks: 0 ONE OF MANY ERRORS IN CALCULUS-2 I will show one real mistake of CALCULUS. We look the link: http://en.wikipedia.org/wiki/Partial_derivative(Examples) We see a formula of a full derivative of volume of a cone on height: $\frac{dV}{dh}=\pi r^2.$ We integrate this derivative and we receive... cylinder volume: $\int dV=\int \pi r^2dh=\pi r^2h.$ Here to you one real mistake!
 December 18th, 2012, 03:27 PM #2 Global Moderator   Joined: May 2007 Posts: 6,558 Thanks: 602 Re: ONE OF MANY ERRORS IN CALCULUS-2 r for a cone is a function of h, r for a cylinder is constant. The integral you wrote is for constant r, so it is wrong for a cone. In a cone r=(H-h)tana, where H is the height of the cone and a is the cone half angle.

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