MAT 1234 Calculus I

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# MAT 1234 Calculus I - PowerPoint PPT Presentation

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 1234Calculus I

Section 3.9

Antiderivatives

http://myhome.spu.edu/lauw

Homework
• WebAssign HW 3.9
• Monday Quiz – 3.8, 3.9
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

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

Formula

where k is a constant

Why?

Formula

Verify

Formula (Linear Property)

where k is a constant

Example 3