Home/Tag: Radians
5 11, 2016

Arc Length

By |2016-11-05T06:38:56+10:00November 5th, 2016|Tags: , , , |0 Comments

Arc Length $$L=\theta\;r$$ worked examples further examples harder examples a. $$8\pi=\frac{2\pi}{3}\times\;r$$ $$24\pi=2\pi\;r$$ r = 12 units b. segment XPY A = ½ r2(θ - sin θ) A = ½ × (12√3)2($$\pi$$/3 - sin $$\pi$$/3) A = 216($$\pi$$/3 - √3/2) u2 A = [...]

12 08, 2015

Simpson’s Rule

By |2016-11-04T20:09:07+10:00August 12th, 2015|Tags: , , , , |0 Comments

Simpson's Rule h/3{f(a) + f(b) + 4(sum of odds) + 2(sum of evens)} worked examples The length of one arch of the curve y = sin x is given by $$\int\limits_0^{\pi } {\sqrt{1+\cos^2\,x}\;dx}$$. Find the approximate length using Simpson's rule with three function values. $$0,\;\frac{\pi}{2},\;\pi$$ find the three [...]

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