1 / 13

6.3

Fundamental Theorem of Calculus. 6.3. The Fundamental Theorem of Calculus. If f is continuous at every point of , and if F is any antiderivative of f on , then. We already know this!. To evaluate an integral, take the anti-derivatives and subtract. p.

elia
Télécharger la présentation

6.3

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. Fundamental Theorem of Calculus 6.3

  2. The Fundamental Theorem of Calculus If f is continuous at every point of , and if F is any antiderivative of f on , then We already know this! To evaluate an integral, take the anti-derivatives and subtract. p

  3. The Fundamental Theorem of Calculus, Part 2 If f is continuous on , then the function has a derivative at every point in , and

  4. 1. Derivative of an integral. The Fundamental Theorem of Calculus, Part 2

  5. First Fundamental Theorem: 1. Derivative of an integral. 2. Derivative matches upper limit of integration.

  6. First Fundamental Theorem: 1. Derivative of an integral. 2. Derivative matches upper limit of integration. 3. Lower limit of integration is a constant.

  7. First Fundamental Theorem: New variable. 1. Derivative of an integral. 2. Derivative matches upper limit of integration. 3. Lower limit of integration is a constant.

  8. The long way: Fundamental Theorem: 1. Derivative of an integral. 2. Derivative matches upper limit of integration. 3. Lower limit of integration is a constant.

  9. 1. Derivative of an integral. 2. Derivative matches upper limit of integration. 3. Lower limit of integration is a constant.

  10. The upper limit of integration does not match the derivative, but we could use the chain rule.

  11. The lower limit of integration is not a constant, but the upper limit is. We can change the sign of the integral and reverse the limits.

  12. Neither limit of integration is a constant. We split the integral into two parts. It does not matter what constant we use! (Limits are reversed.) (Chain rule is used.)

  13. Homework P318 #1-14 all

More Related