Mat 1234 calculus i
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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.

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MAT 1234 Calculus I

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Mat 1234 calculus i

MAT 1234Calculus I

Section 3.9

Antiderivatives

http://myhome.spu.edu/lauw


Homework

Homework

  • WebAssign HW 3.9

  • Monday Quiz – 3.8, 3.9


Tomorrow

Tomorrow

  • 9.4


Preview

Preview

  • Introduce antiderivatives

  • Introduce the notations from section 4.4 (Indefinite integral)


Reverse operation of differentiation

Reverse Operation of Differentiation

f’(x)=g(x)

g(x) is thederivative of f(x)

f(x) is anantiderivative of g(x)


Example 1

Example 1

is the derivative of

is an antiderivative of


Example 11

Example 1

is the derivative of functions of the form


Q is it possible

Q: Is it possible…

is the derivative of functions of the form


Consequence of the mvt

Consequence of the MVT

a

b


Example 12

Example 1

The most general antiderivative

The antiderivative of

is of the form

Arbitrary constant


Notation indefinite integral

Notation (Indefinite Integral)

The notation always comes in pair.


Notation

Notation

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


Notation1

Notation

Always use parentheses if there is a sum/difference


Formal definition

Formal Definition

If then


Formula

Formula

where k is a constant

Why?


Formula1

Formula

Verify


Example 2

Example 2


Formula linear property

Formula (Linear Property)

where k is a constant


Example 3

Example 3

Tradition


Example 4

Example 4


Example 5

Example 5


Example 6

Example 6


Example 7

Example 7


Formula2

Formula


Example 8

Example 8


Example 9

Example 9

If and , find .


Caution

Caution


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