Calculus 22

Calculus

Lesson 22 Riemann Sums

We have seen that .

The sum, , is called a "Riemann Sum." It is often useful to write

out a Riemann Sum before we write out the integral.

Definition:

So,

We are going to focus on setting up the integrals for now - that's all!!!! We will

start evaluating the integrals in the next section.

For each of the following examples, plot the graph, show the

differential area, set up Riemann Sum, and then change

into an integral.

Let's find the area under the curve on the interval .

Plot it!

By definition, the answer is .

There are many ways to express this area!

The first is the original, the second is negative since dx is moving backward,

the third shows that area can be added piece by piece, the fourth shows that

area can be added function by function (show graphs of x and 2x).

Other examples:

for a variety of intervals.

We will evaluate them next time!!!!!

On to Lesson 23 - FTC and MVT for Integrals