# MAT 1221 survey of Calculus Section 6.1 Antiderivatives and Indefinite Integrals

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MAT 1221 survey of Calculus Section 6.1 Antiderivatives and Indefinite Integrals http://myhome.spu.edu/lauw

Expectation Simplify your answers. For problem 2: Formally answer the question in full sentence Pay attention to the units

Preview Introduce antiderivatives/ indefinite integral Introduce integration formulas Initial Value Problems Word Problems

Reverse Operation of Differentiation

Example 1 is the derivative of is an antiderivative of

Example 1 is the derivative of functions of the form

Example 1 The antiderivative of is of the form

Notation

Differential Integral Sign

Notation Constant of Integration/ Arbitrary Constant Integrand

Notation The notation always comes in pair.

Notation

Formal Definition

Formula Why?

Formula Verify

Example 2

Formula

Example 4

Remark on the integral notation Use parenthesis if there are two or more terms in a sum or difference.

Example 5

Example 6

Example 7

Caution

Differential Equations and Initial Conditions

Differential Equations and Initial Condition

Formula

The antiderivative of the derivative is the original function.

Example 8

Example 9

(b) Find the area of the wound after 7 days. The area of the wound after 7 days is cm 2

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