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Sec 5.4:INDEFINITE INTEGRALS AND THE NET CHANGE THEOREM

Note1: is traditionally used for an antiderivative of Note2: is called an indefinite integral Example:

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Sec 5.4:INDEFINITE INTEGRALS AND THE NET CHANGE THEOREM

The connection between them

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Sec 5.4:INDEFINITE INTEGRALS AND THE NET CHANGE THEOREM

Table Indefinite Integrals

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Sec 5.4:INDEFINITE INTEGRALS AND THE NET CHANGE THEOREM

Table Indefinite Integrals

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TERM-092 Sec 5.4:INDEFINITE INTEGRALS AND THE NET CHANGE THEOREM

Table Indefinite Integrals

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TERM-092 Sec 5.4:INDEFINITE INTEGRALS AND THE NET CHANGE THEOREM

Table Indefinite Integrals

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TERM-092 Sec 5.4:INDEFINITE INTEGRALS AND THE NET CHANGE THEOREM

Table Indefinite Integrals Remark

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TERM-092 Sec 5.4:INDEFINITE INTEGRALS AND THE NET CHANGE THEOREM

Table Indefinite Integrals

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TERM-082 Sec 5.4:INDEFINITE INTEGRALS AND THE NET CHANGE THEOREM

Table Indefinite Integrals

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TERM-082 Sec 5.4:INDEFINITE INTEGRALS AND THE NET CHANGE THEOREM

Table Indefinite Integrals

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Sec 5.4:INDEFINITE INTEGRALS AND THE NET CHANGE THEOREM

Table Indefinite Integrals

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Sec 5.4: THE NET CHANGE THEOREM

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Sec 5.4:INDEFINITE INTEGRALS AND THE NET CHANGE THEOREM

Example1:

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Sec 5.4:INDEFINITE INTEGRALS AND THE NET CHANGE THEOREM

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Sec 5.4:INDEFINITE INTEGRALS AND THE NET CHANGE THEOREM

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Sec 5.4:INDEFINITE INTEGRALS AND THE NET CHANGE THEOREM

Motion Along a Line: Displacement Suppose that an object is moving along a coordinate line, usually horizontal or vertical, so that we know its position s on that line as a function of time t: Example1: If at time t, the position of a body moving along the s- axis is 1) net change of position, or displacement = 2) total distance traveled total distance = Example2: If at time t, the velocit of a body moving along the s- axis is net change of position, or displacement during the period [t1, t2] is total distance traveled during the period [t1, t2] is

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Sec 5.4:INDEFINITE INTEGRALS AND THE NET CHANGE THEOREM

Motion Along a Line: Displacement Suppose that an object is moving along a coordinate line, usually horizontal or vertical, so that we know its position s on that line as a function of time t: Example1: If at time t, the position of a body moving along the s- axis is 1 2 3 4 5 18 22 20 net change of position, or displacement = total distance traveled = Example2: If at time t, the velocit of a body moving along the s- axis is net change of position, or displacement during the period [t1, t2] is total distance traveled during the period [t1, t2] is

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total distance traveled

Sec 5.4:INDEFINITE INTEGRALS AND THE NET CHANGE THEOREM displacement If an object moves along a straight line with position function , then its velocity is the net change of position, or displacement, total distance traveled

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Sec 5.4:INDEFINITE INTEGRALS AND THE NET CHANGE THEOREM

displacement total distance

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Sec 5.4:INDEFINITE INTEGRALS AND THE NET CHANGE THEOREM

The integral of a rate of change is the net change: represents the net change in

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Sec 5.4:INDEFINITE INTEGRALS AND THE NET CHANGE THEOREM

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