4.1A Antiderivatives

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4.1A Antiderivatives
A function F is the Antiderivative of f if F
?(x) f (x) for all x.
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• Ex 1 Find the Antiderivative

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Power Rule
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NOTE see pg. 250 for more Antiderivative Rules
Ex 2 Find all functions g such that
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Ex 3 Evaluate
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Ex 4 Evaluate
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Ex 5 Make a rough sketch of the antiderivative
F, given that F(0) 2, the sketch of f.
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Ex 6 Find f such that f (0) ?2 and
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HW 4.1A pg. 255 9 41 odds, 43 47
all, 55, 59
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4.1B Position, Velocity, Acceleration
NOTE Acceleration due to gravity is ? ?9.8
m/s2 OR ?32 ft/s2
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The Total Change Theorem The integral of a
rate of change is the total change.
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Ex 1 A particle moves along a line so that its
velocity at time t is v(t) t2 t 6
(m/sec). a) Find the displacement from t 1 to
4 seconds.
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Ex 1 A particle moves along a line so that its
velocity at time t is v(t) t2 t 6
(m/sec). b) Find the distance traveled during
this time period.
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Displacement Total Change in Position
Distance
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Ex 2 A ball is thrown upward with a speed of 48
ft/s from the edge of a 432 ft. cliff. a)
Find h(t) where h is height in feet t is
time in seconds. b) When does it reach its max
height? c) When does it hit the ground?
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Ex 3 A particle has an acceleration given by
a(t) 6t 4. Its initial velocity is v(0) ?6
cm/s and its initial displacement is s(0) 9 cm.
Find the function s(t).
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HW 4.1B pg. 255 65 85 odds, 94