The Trapezoidal Rule
It is the method of approximation a difinite integral with using trapezoids.
Assume that f is ontinuous and positive on the interval [a,b].
So, the definite integral f(x) a to b as x values represents the area of the region bounde by
the graph of f and the x-axis, from x=a to x=b.
By adding these trapezoids up, you can approximate integrations.
![(1/2)*(b-a)*(f(x[0])+2*f(x[1])+2*f(x[2])+`...`+2*f(x[N-1])+f(x[N]))/N](http://www.maplesoft.com/view.aspx?si=108805/file04105/math168.png)
Here are examples.
with(Student[Calculus1]);
>ApproximateInt(sin(x),x=0..π, method=trapezoid, output=plot)
As n, the number of subintervals, is going to infinity,
approximation of an integral approaches its real value.
with(Student[Calculus1]);
>ApproximateInt(sin(x),x=0..π, method=trapezoid, output=animation)
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