“What is a more accurate way for approximating integrals?”
If we have a particular function, then there are many simple ways to approximate the area under the curve without integrating. However, is there a more accurate way to do this? Well, let’s use our mathematical mindset to find out. If we were to fit a third-degree polynomial over our function and then take its integral, we would arrive with an area very close. This method is known in the English speaking world as Simpson’s Rule, and is represented by the formula Area = (b-a)/6 * ( f(a) + 4f((a+b)/2) + f(b) ), with a being the start point and b being the endpoint.