Mathematical Sciences
MATH 2109 { Mathematical Computing
Assignment 2 Due 12 : 00 pm Monday 11th May 2020.
The vast majority of definite integrals cannot be evaluated analytically (i.e., symbolically). Numerical integration (quadrature) may be used to approximate definite integrals. There are many
quadrature methods including: Left-hand sums, Trapezoidal rule, Simpson’s rule, Midpoint rule.
The Midpoint rule approximates the integral under the function f over the interval [xk; xk+1] by
Ak = yk∗hk.
where hk = xk+1 – xk, yk∗ = f(x∗ k), and x∗ k is the midpoint of the subinterval [xk; xk+1] (i.e.,
x∗
k =
xk+xk+1
2 ). We consider a Modified Midpoint rule which approximates the integral over interior
subintervals by the average of the integrals over the interior subinterval and the two adjacent
subintervals. The the formula for the Modified Midpoint ruls is
Zab f(x) dx ≈ A = A1 + A1 + A32 + A3 + A2 + A33 + A4 +
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