Riemann sums
Download
1 / 16

Riemann Sums - PowerPoint PPT Presentation


  • 175 Views
  • Uploaded on

Riemann Sums. Width of partition:. Adds the rectangles, where n is the number of partitions (rectangles). Height of rectangle for each of the x-values in the interval. What is a Riemann Sum?. Takes approximating the area under a curve with rectangles to the next level LOOKS LIKE:.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Riemann Sums' - tarmon


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

What is a riemann sum

Width of partition:

Adds the rectangles, where n is the number of partitions (rectangles)

Height of rectangle for each of the x-values in the interval

What is a Riemann Sum?

  • Takes approximating the area under a curve with rectangles to the next level

    LOOKS LIKE:


What do we do with this
What Do We Do With This?

If the number of partitions is allowed to approach infinity…what happens?

That’s right! The rectangular approximation approaches the EXACT area under the curve! How do we do it?



What in the world
What in the World?

READ LIKE THIS:

The integral, from a to b, of f(x) with respect to x


What s with this thing
What’s With This Thing?

Integrand (between the integral sign and the dx)

Upper (right) limit of integration

Integral sign (originated from the summation sign, Sigma)

Lower (left) limit of integration

Tells you the variable of integration (who is the variable)


Examples of how to read
Examples of How to Read

  • The integral, from 1 to 4, of x2 with respect to x is 21


Writing riemann sums as integrals
Writing Riemann Sums as Integrals

Where x is between 0 and 2.


Writing riemann sums as integrals1
Writing Riemann Sums as Integrals

Where x is between 3 and 7.


Writing riemann sums as integrals2
Writing Riemann Sums as Integrals

Where x is between -2 and 2.


Definite integrals

Definite Integrals

Why is it called a definite integral?

Because the integral sign includes limits of integration!




Properties of definite integrals2
Properties of Definite Integrals

Why?

  • Because the integral is asking for the area under the curve between 2 and 2…there is no area covered!


Properties of definite integrals3
Properties of Definite Integrals

Why is this okay?

  • Because an integral is just a limit of a Riemann Sum…so all the properties of limits hold for integrals!



ad