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## PowerPoint Slideshow about ' MAT 1234 Calculus I' - mahon

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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 functions of the form

Q: Is it possible…

is the derivative of functions of the form

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

Verify

Formula (Linear Property)

where k is a constant

Example 3

Tradition

Example 9

If and , find .

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