1 / 8

Section 6.1 Antiderivatives Graphically and Numerically

Section 6.1 Antiderivatives Graphically and Numerically. The following is a velocity curve in ft/sec How would we find the distance traveled between 0 and 2 seconds?. The following is a velocity curve in ft/sec How would we find the distance traveled between 2 and 4 seconds?.

dea
Télécharger la présentation

Section 6.1 Antiderivatives Graphically and Numerically

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 6.1Antiderivatives Graphically and Numerically

  2. The following is a velocity curve in ft/sec • How would we find the distance traveled between 0 and 2 seconds?

  3. The following is a velocity curve in ft/sec • How would we find the distance traveled between 2 and 4 seconds?

  4. The following is a velocity curve in ft/sec • How would we find the total distance traveled in the first 4 seconds?

  5. The following is a velocity curve in ft/sec • Thus we can use the area under the curve to give us the change in function values

  6. In the last section we began discussing area under a curve • If we had a velocity curve than the area under the curve gave us the distance traveled • We introduced the definite integral as a way of finding the net area under a curve • The net area under the curve gives us the change in the function value from a to b • We are going to use this information to see how we can recover function values give the derivative

  7. Complete the worksheet • Find the area under f’ between 0 and 3 • Now use the Fundamental Theorem of Calculus to get the area under each graph you found between 0 and 3 • f and g are called antiderivatives of f’ • They have the same derivative, although they are different functions

  8. Given the values of the derivative, f’(x) in the table and that f(0) = 100, estimate f(x) for x = 2, 4, 6.

More Related