Approximation of Integration (The Trapezoidal Rule)

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.



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)