Multivariable calculus 3.1 - Repetition of 1d integrals

Описание: The third block in the series is about integration in multivariable calculus. This first video will be a repetition of the integral in 1d, with focus on what the integral is (using the Riemann sum), and then some techniques for solving them, such as integration by parts and substitutions.
At the end, we will also talk about how to move the derivative inside the integral, and a small introduction to integrals in multivariable calculus, as we will look at how to reconstruct a scalar field, if we know the gradient of it.

Note: I will do short derivations of why the integrals work, to make it easier to follow then for later stages when we repeat the same steps in multivariable calculus. These derivations should only be considered as motivations as I will not provide strict proofs of it (i.e. not show that all errors actually goes to zero)

0:00 Introduction, what is the integral
2:26 Riemann sum
8:26 Opposite direction
9:29 Split interval
10:31 Antiderivative
11:36 Integration by parts
13:55 Substitutions
17:42 Substitutions - integrate x*exp(-x^2)
19:36 Derivative inside integral
22:27 Integrals and partial derivatives (gradient)