Loading in 5 sec....

Fundamental theorem of calculus IIPowerPoint Presentation

Fundamental theorem of calculus II

- By
**pepin** - Follow User

- 77 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about ' Fundamental theorem of calculus II' - pepin

**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

Integrate

Area under the curve

Fundamental theorem of calculus I

Change of variables

Fundamental theorem of calculus II

Verify that this sum makes sense. There are values of Dx that break this picture. What are they?

0

STOP

“Definite integral”

0

STOP

We wrote a differential. What is coordinately shrinking with ?

If we hold a in place, the derivative of A “happens” to be

0

STOP

Differentiation “undoes” integration. Do you remember why?

Integrate

Area under the curve

Fundamental theorem of calculus I

Change of variables

Fundamental theorem of calculus II

Integrate

Area under the curve

Fundamental theorem of calculus I

Change of variables

Fundamental theorem of calculus II

Generic differentiation rule

Notion of anti-derivative:Instead of maligning the indefinite integral as the result of “forgetting” to write down symbols in a definite integral, one often says that, in the context of an equation lacking beginning and end points, such as , the “curvy S” indicates merely that taking the derivative of gives . This kind of use of language does not require discussion of the notion of area under a curve.

STOP

Integrate

Area under the curve

Fundamental theorem of calculus I

Change of variables

Fundamental theorem of calculus II

Change of variables example: Trigonometric functions

Choose to identify

Find in integration table:

0

Integrate

Area under the curve

Fundamental theorem of calculus I

Change of variables

Fundamental theorem of calculus II

Download Presentation

Connecting to Server..