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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 1234Calculus I

Section 3.9

Antiderivatives

http://myhome.spu.edu/lauw

### Homework

• WebAssign HW 3.9

• Monday Quiz – 3.8, 3.9

• 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

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

a

b

### 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

If then

### Formula

where k is a constant

Why?

Verify

### Formula (Linear Property)

where k is a constant

If and , find .