The Definite Integral Let’s review what we saw in part 1:
The Definite Integral Let’s review what we saw in part 1: V t
The Definite Integral Let’s review what we saw in part 1: V t dt
The Definite Integral Let’s review what we saw in part 1: V ≈ constant! Vdt t dt
The Definite Integral Let’s review what we saw in part 1: V t
The Definite Integral Let’s review what we saw in part 1: V t t 0
The Definite Integral Let’s review what we saw in part 1: V t t 0
The Definite Integral Let’s review what we saw in part 1: V t t 0
The Definite Integral Let’s review what we saw in part 1: V t t 0 The area under the curve gives us the distance traveled.
Notation We saw that the distance traveled during each small interval is:
Notation We saw that the distance traveled during each small interval is: ds = Vdt
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.
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 .
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:
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: � t 0 s = Vdt 0
Notation The definite integral is the area under the curve:
Notation The definite integral is the area under the curve: V t t 0 this area approaches s � t 0 s = Vdt 0
Notation The definite integral is the area under the curve: V t t 0 this area approaches s � t 0 s = Vdt 0
Notation The definite integral is the area under the curve: V t t 0 this area approaches s � t 0 s = Vdt 0
Notation The definite integral is the area under the curve: V t t 0 this area is s ! � t 0 s = Vdt 0
Notation
Notation � t 1 t 0
Notation � t 1 infinite sum! t 0
Notation � t 1 infinite sum! t 0 lower limit
Notation upper limit � t 1 infinite sum! t 0 lower limit
Notation � t 1 f ( x ) dx t 0
Notation � t 1 f ( x ) dx � �� � t 0 area of small rectangle
Notation � t 1 f ( x ) dx � �� � t 0 area of small rectangle V ≈ constant! Vdt t dt
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