1 / 9

Section 4.3 Riemann Sums and Definite Integrals

Section 4.3 Riemann Sums and Definite Integrals. Section 4.3 Riemann Sums and Definite Integrals.

gannon-potter
Download Presentation

Section 4.3 Riemann Sums and Definite Integrals

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. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Section 4.3 Riemann Sums and Definite Integrals

  2. Section 4.3 Riemann Sums and Definite Integrals • To this point, anytime that we have used the integral symbol we have used it without any upper or lower boundaries. In other words, it has served as simply a short hand symbol asking you to antidifferentiate a function. • We have also been talking about areas simultaneously. Those problems do have upper and lower bound limits. • There is a reason that we have been pursuing these two seemingly different goals at the same time.

  3. Section 4.3 Riemann Sums and Definite Integrals • The reason why is that they are the same goal, not different ones. • Using words to describe a problem: • Find the area of the region bounded by the curve ,the x-axis, and the lines x = 2 and x = 6. • Using summation to describe the problem • Using integral notation to describe the problem

  4. Section 4.3 Riemann Sums and Definite Integrals • Below is a visual representation of the region bounded by the curve and the vertical boundaries.

  5. Section 4.3 Riemann Sums and Definite Integrals • Draw the region defined by the integral below:

  6. Section 4.3 Riemann Sums and Definite Integrals • Did your graph look like the one below?

  7. Section 4.3 Riemann Sums and Definite Integrals • Now try to read a summation notation and turn it into a picture AND into a definite integral. Here’s the sigma notation:

  8. Section 4.3 Riemann Sums and Definite Integrals • Does your picture look like this?

  9. Section 4.3 Riemann Sums and Definite Integrals • Does your integral look like this?

More Related