Our technique so far for finding a definite integral (an integral with limits of integration) requires that we find an antiderivative of the integrand. This is not always possible. Mathematicians can prove that there is no closed form for an antiderivative for e^x2. That is, no formula (without an integral sign in it) whose derivative is e^x2.

Some calculators and computers can find very good approximations to definite integrals of this type. They use techniques that are based on special cases of Riemann sums to obtain these approximations.

We will explore the approximation techniqes called the Midpoint Rule, the Trapezoidal Rule, and Simpson's Rule.