Course description

Build the integral from the ground up by treating area as a real quantity, with every graph standing for something worth counting: labor cost, energy used by an appliance, distance traveled, volume of water in a tank. By the end of the course, you'll be able to estimate the area under any curve with Riemann sums, evaluate definite integrals exactly, use the Fundamental Theorem of Calculus to turn an area problem into an antiderivative, integrate polynomials, trigonometric and exponential functions using substitution and integration by parts, and apply all of it to areas between curves, volumes of solids, and integrals over infinite domains. You'll see where each technique comes from instead of memorizing a table of rules.