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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 Spring '16
 Alveen Chand
 Numerical Analysis, Approximation, dx, Imation

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