MTH405_Wk_11_Tutorial

# MTH405_Wk_11_Tutorial - MTH405 Wk 11 Tutorial Numerical...

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Unformatted text preview: MTH405 Wk 11 Tutorial Numerical Integration Notes • Midpoint Approximation: ˆ b  f (x)dx = Mn = a here n m1 , m2 , . . . , mn b−a n [a, b] and [a, b]. Trapezoidal Approximation: ˆ b  f (x)dx = Tn = a • [f (m1 ) + f (m2 ) + . . . + f (mn )] are midpoints of the subintervals of is the number of divisions of •  b−a 2n  [y0 + 2y1 + . . . + 2yn−1 + yn ] . Simpsons Approximation: S2n 1 = 3  b−a 2n  [y0 + 4y1 + 2y2 + 4y3 + 2y4 + . . . + 2y2n−2 + 4y2n−1 + y2n ] . Exercise. 1. Use n=5 subintervals to approximate the integrals by Mid- point approximation, Trapezoidal approximation and Simpsons approximation. ´2 (x2 + 1) dx 1 ´ 1 −x2 e dx (b) 0 ´2 x √ dx (c) 0 1+x2 ´2√ (d) x3 − 1dx 1 (a) 1 ...
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