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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

• WebAssign HW 3.9

• Monday Quiz – 3.8, 3.9

• 9.4

• Introduce antiderivatives

• Introduce the notations from section 4.4 (Indefinite integral)

f’(x)=g(x)

g(x) is thederivative of f(x)

f(x) is anantiderivative of g(x)

is the derivative of

is an antiderivative of

is the derivative of functions of the form

is the derivative of functions of the form

The most general antiderivative

The antiderivative of

is of the form

Arbitrary constant

The notation always comes in pair.

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

Always use parentheses if there is a sum/difference

If then

where k is a constant

Why?

Verify

where k is a constant