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Task/Numerical-integration/00DESCRIPTION

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+Write functions to calculate the definite integral of a function (<span style="font-family: serif">''f(x)''</span>) using [[wp:Rectangle_method|rectangular]] (left, right, and midpoint), [[wp:Trapezoidal_rule|trapezium]], and [[wp:Simpson%27s_rule|Simpson's]] methods. Your functions should take in the upper and lower bounds (<span style="font-family: serif">''a''</span> and <span style="font-family: serif">''b''</span>) and the number of approximations to make in that range (<span style="font-family: serif">''n''</span>). Assume that your example already has a function that gives values for <span style="font-family: serif">''f(x)''</span>.
+
+Simpson's method is defined by the following pseudocode:
+<pre>
+h := (b - a) / n
+sum1 := f(a + h/2)
+sum2 := 0
+
+loop on i from 1 to (n - 1)
+    sum1 := sum1 + f(a + h * i + h/2)
+    sum2 := sum2 + f(a + h * i)
+
+answer := (h / 6) * (f(a) + f(b) + 4*sum1 + 2*sum2)
+</pre>
+
+Demonstrate your function by showing the results for:
+* f(x) = x^3, where x is [0,1], with 100 approximations. The exact result is 1/4, or 0.25.
+* f(x) = 1/x, where x is [1,100], with 1,000 approximations. The exact result is the natural log of 100, or about 4.605170
+* f(x) = x, where x is [0,5000], with 5,000,000 approximations. The exact result is 12,500,000.
+* f(x) = x, where x is [0,6000], with 6,000,000 approximations. The exact result is 18,000,000.
+
+'''See also'''
+* [[Active object]] for integrating a function of real time.
+* [[Numerical integration/Gauss-Legendre Quadrature]] for another integration method.