Riemann Sum Calculator

Pick an integrand from the menu, set the limits and the number of subintervals, and this tool returns the left, right, midpoint and trapezoidal sums together, along with Simpson's rule when n is even. Each one is printed with its signed error against the exact value, which comes from the antiderivative rather than from a finer approximation of the same kind. The rule you choose is drawn as strips under the curve so you can see where each subinterval gains or loses area. A second tab doubles n five times and tabulates the errors, which is where the left and right sums show themselves to be first-order and the midpoint and trapezoidal sums second-order.