3 Integrals You Won't See in Calculus (And the 2 You Will)

In Calculus, we usually learn the Riemann integral, or sometimes the Darboux integral in disguise. But there are many problems these integrals can't solve! Like if we want to integrate a function which is discontinuous everywhere, or if we want to integrate with respect to a random process. Let's explore 5 different integrals, starting with the 2 you might see in Calculus, and then 3 more advanced integrals that are often only seen in graduate school -- the Riemann-Stieltjes integral, Lebesgue integral, and Itô integral! 00:00 Introduction 00:32 Level 1 -- Riemann Integral 01:58 Level 2 -- Darboux Integral 04:00 Level 3 -- Riemann-Stieltjes 07:02 Level 4 -- Lebesgue Integral 09:57 Level 5 -- Itô Integral