1. Note that when you rotate the line through the midpoint, the area under that line does not change.[br][br]2. When point D is very close to point C, then[br](Error in the Trapezoid Rule )+2*(Error in the Mid-point Rule) [math]\approx[/math] 0.[br][br]Thus, we can reduce the error by taking the weighted average:[br]Simpson's Approximation [math]\approx[/math] [math]\frac{1}{3}[/math] (Trapezoid Approximation )+[math]\frac{2}{3}[/math](Mid-point Approximation)