Trapezoidal Rule Calculator

The trapezoidal rule replaces a curve with straight chords between evenly spaced points and adds up the strips, which is why the answer drifts high on a curve bending upwards and low on one bending downwards. Give a polynomial by its coefficients, or pick one of six standard integrands, choose the limits and the number of subintervals, and the tool returns the approximation, the exact integral, the real error and the classical bound with the value of M it used. A third mode takes a table of x and y readings, evenly spaced or not, and integrates them directly. For measured points there is no formula behind the data, so that mode gives the area and says plainly that no error estimate is possible.