MTH405_Wk_11_Lect_1

# MTH405_Wk_11_Lect_1 - MTH405 Wk 11 Lect 1 Midpoint...

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Unformatted text preview: MTH405 Wk 11 Lect 1 Midpoint Approximation Exercise. Evaluate ´3 1 (x2 + 1)dx where n=4 using Midpoint Ap- proximation. Trapezoidal Approximation Also known as Trapeziodal Rule. The formula to use are: width of the subintervals, ˆ b f (x)dx ≈ Tn = Area function a Example. 1. Evaluate imation. 2. Evaluate ´2 1 ´3 1 (x3 + 1)dx ∆x = b−a n 1 [y0 + 2y1 + 2y2 + . . . + 2yn−1 + yn ]·∆x 2 where n=4 using Trapezoidal Approx- (x2 + x)dx where n = 4 using Trapezoidal Approx- imation. Simpsons Approximation Also known as Simpsons Rule. The formula to use is: ˆ b f (x)dx ≈ S2n a Example. 1. Evaluate mation. 2. Evaluate ´2 1 ´3 1 1 = 3  b−a 2n    y0 + 4y1 + 2y2 + 4y3 + 2y4 + . . . + 4y(2n)−1 + y2n . (x3 + 1)dx where n=4 using Simpsons Approxi- (x2 + x)dx where n=4 using Simpsons Approxi- mation. 1 ...
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