08 - ApproxInt

# 08 - ApproxInt - Ex Approximate sin e x 1 2 ± dx n = 6 x...

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Trapezoid Rule We have used a left and right Riemann sum to approximate an integral. Now we will introduce two more methods of approximation – the Trapezoid Rule and Simpson’s Rule. Trapezoid Rule: Instead of rectangles, we will use trapezoids to approximate the area.

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The Trapezoid Approximation = LRS+RRS 2 Ex. Approximate sin e x ) 1 2 dx , n = 5 x f(x)
Ex. Approximate x dx 1 4 , n = 3 Simpson’s Rule: Use parabolas to estimate the area. For parabolas, we must use two intervals so n will always be even.

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Unformatted text preview: Ex. Approximate sin e x 1 2 ± dx , n = 6 x f(x) Ex. Approximate x ± dx 1 4 , n = 4 Do: 1 Find the trapezoid rule approximation to f ( x )± dx-3 , using the following table of values. x-3-2.5-2-1.5-1-.5 f(x) 2 1 1 1 2 3 2. Find the Simpson’s rule approximation to the integral for the function on the given interval, using the same table of values. 3. Set up a Simpson’s rule approximation for x x ± dx ,± n 4 3 9 . Do not evaluate....
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