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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

MAT 1234Calculus I

Section 3.9

Antiderivatives

http://myhome.spu.edu/lauw


Homework
Homework

  • WebAssign HW 3.9

  • Monday Quiz – 3.8, 3.9



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



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



Formula
Formula

where k is a constant

Why?


Formula1
Formula

Verify



Formula linear property
Formula (Linear Property)

where k is a constant


Example 3
Example 3

Tradition








Example 9
Example 9

If and , find .



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