Antidifferentiation!
What’s that? Well, it’s the antiderivative or the derivative in reverse.
But that’s a mouthful to say, don’t you think? Thankfully, another way of saying antiderivative is the term Indefinite Integral, or simply, Integration.
Now, Integration, as we will soon discover, is more than just finding all solutions for a derivative (differential equation), it’s used to calculate the area of a plane region!
This amazing process is called Riemann Sums, sometimes called numerical integration.
As the German mathematician so famously discovered, the easiest way to find the area of any region is to subdivide it into simple geometric shapes, namely rectangles, and then add (sum up) all of these rectangular areas.
Finding Areas and Distances
Together, we will see how easy it is to find the area bounded by a graph by partitioning the region into either rectangular or trapezoidal subintervals.
We will learn the notation and formulas for finding the Right and Left Rieman Sums (also known as the upper and lower sums), as well as the Midpoint Rule and the Trapezoidal Rule.
All of these techniques help us to create the building blocks for our Integration rules and properties and allows us to formally define the Definite Integral, which is the infinite limit of our summations.
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