Riemann sums and the trapezium rule are both techniques for approximating the area under a curve, which is a fundamental idea in integral calculus. A Riemann sum works by dividing the area under a curve into several rectangles and summing their areas. Depending on where the height of each rectangle is taken—left endpoint, right endpoint, or midpoint—you get different types of Riemann sums. The trapezium (or trapezoidal) rule takes a slightly different approach by approximating the area using tra