Mat 1234 calculus i
Sponsored Links
This presentation is the property of its rightful owner.
1 / 27

MAT 1234 Calculus I PowerPoint PPT Presentation


  • 60 Views
  • Uploaded on
  • Presentation posted in: General

MAT 1234 Calculus I. Section 3.9 Antiderivatives. http://myhome.spu.edu/lauw. Homework. WebAssign HW 3.9 Monday Quiz – 3.8, 3.9. Tomorrow. 9.4. Preview. Introduce antiderivatives Introduce the notations from section 4.4 (Indefinite integral). Reverse Operation of Differentiation.

Download Presentation

MAT 1234 Calculus I

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


MAT 1234Calculus I

Section 3.9

Antiderivatives

http://myhome.spu.edu/lauw


Homework

  • WebAssign HW 3.9

  • Monday Quiz – 3.8, 3.9


Tomorrow

  • 9.4


Preview

  • Introduce antiderivatives

  • Introduce the notations from section 4.4 (Indefinite integral)


Reverse Operation of Differentiation

f’(x)=g(x)

g(x) is thederivative of f(x)

f(x) is anantiderivative of g(x)


Example 1

is the derivative of

is an antiderivative of


Example 1

is the derivative of functions of the form


Q: Is it possible…

is the derivative of functions of the form


Consequence of the MVT

a

b


Example 1

The most general antiderivative

The antiderivative of

is of the form

Arbitrary constant


Notation (Indefinite Integral)

The notation always comes in pair.


Notation

If the independent variable is in u, then the differential is du


Notation

Always use parentheses if there is a sum/difference


Formal Definition

If then


Formula

where k is a constant

Why?


Formula

Verify


Example 2


Formula (Linear Property)

where k is a constant


Example 3

Tradition


Example 4


Example 5


Example 6


Example 7


Formula


Example 8


Example 9

If and , find .


Caution


  • Login