Textbook Guide Mathematics: Density, Marginal Cost, Hydrostatics
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MAT133Y1 Full Course Notes
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Arc length: the length l of c is approximately the length of this polygon and the approximation gets better as we let n increase, it can be expressed as: If we use leibniz notation for derivatives, we can write the arc length formula as follows: In the case where f is positive and has a continuous derivative, we define the surface area of the surface obtained by rotating the curve y = f(x), a x b, about the x-axis as. With the leibniz notation for derivatives, this formula becomes. If the curve is described as x=g(y), c y d, then the formula for surface area becomes. They can be summarized symbolically, using the notation for arc length: For rotation about the y-axis, the surface area formula becomes. Hydrostatics: the pressure in any direction at a depth d in a fluid with mass density is given by.
