Trapezoid Integration

The Trapezoid Integration Method uses right trapezoids to approximate the curve. The area of these trapezoids can be broken down into the area of a square plus the area of a triangle:

f(x)*dx + 0.5*(f(x)-f(x+dx))*dx, which simplifies to:

0.5*(f(x)+f(x+dx))*dx

Notice that the Trapezoid Integration Method is numerically equivalent to the Average Riemann Sum.