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The Definite Integral Lets review what we saw in part 1: The - - PowerPoint PPT Presentation
The Definite Integral Lets review what we saw in part 1: The - - PowerPoint PPT Presentation
The Definite Integral Lets review what we saw in part 1: The Definite Integral Lets review what we saw in part 1: V t The Definite Integral Lets review what we saw in part 1: V t dt The Definite Integral Lets review what we
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The Definite Integral
Let’s review what we saw in part 1: t V
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The Definite Integral
Let’s review what we saw in part 1: dt t V
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The Definite Integral
Let’s review what we saw in part 1: dt ≈ constant! t V Vdt
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The Definite Integral
Let’s review what we saw in part 1: t V
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The Definite Integral
Let’s review what we saw in part 1: t V t0
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The Definite Integral
Let’s review what we saw in part 1: t V t0
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The Definite Integral
Let’s review what we saw in part 1: t V t0
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The Definite Integral
Let’s review what we saw in part 1: t V t0 The area under the curve gives us the distance traveled.
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Notation
We saw that the distance traveled during each small interval is:
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Notation
We saw that the distance traveled during each small interval is: ds = Vdt
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Notation
We saw that the distance traveled during each small interval is: ds = Vdt And the distance over a longer interval is the sum of these small distances.
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Notation
We saw that the distance traveled during each small interval is: ds = Vdt And the distance over a longer interval is the sum of these small distances. Taking the limit as the width of these intervals approches zero, we get the definite integral.
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Notation
We saw that the distance traveled during each small interval is: ds = Vdt And the distance over a longer interval is the sum of these small distances. Taking the limit as the width of these intervals approches zero, we get the definite integral. We write this limit as:
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Notation
We saw that the distance traveled during each small interval is: ds = Vdt And the distance over a longer interval is the sum of these small distances. Taking the limit as the width of these intervals approches zero, we get the definite integral. We write this limit as: s = t0 Vdt
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Notation
The definite integral is the area under the curve:
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Notation
The definite integral is the area under the curve: t V t0 this area approaches s s = t0 Vdt
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Notation
The definite integral is the area under the curve: t V t0 this area approaches s s = t0 Vdt
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Notation
The definite integral is the area under the curve: t V t0 this area approaches s s = t0 Vdt
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Notation
The definite integral is the area under the curve: t V t0 this area is s! s = t0 Vdt
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Notation
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Notation
t1
t0
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Notation
t1
t0
infinite sum!
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Notation
t1
t0
infinite sum! lower limit
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Notation
t1
t0
infinite sum! lower limit upper limit
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Notation
t1
t0
f (x)dx
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Notation
t1
t0
f (x)dx area of small rectangle
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Notation
t1
t0
f (x)dx area of small rectangle dt ≈ constant! t V Vdt
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