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Miss Battaglia AB/BC Calculus.  Connects differentiation and integration.  Integration & differentiation are inverse operations. If a function is continuous.

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Presentation on theme: "Miss Battaglia AB/BC Calculus.  Connects differentiation and integration.  Integration & differentiation are inverse operations. If a function is continuous."— Presentation transcript:

1 Miss Battaglia AB/BC Calculus

2  Connects differentiation and integration.  Integration & differentiation are inverse operations. If a function is continuous on the closed interval [a,b] and F is an antiderivative of f on the interval [a,b], then

3 1. Provided you can find an antiderivative of f, you now have a way to evaluate a definite integral without having to use the limit of a sum. 2. When applying the FTC, the following notation is convenient For instance, to evaluateyou can write 3. It is not necessary to include a constant of integration C in the antiderivative because

4 a. b. c.

5 Evaluate

6 Find the area of the region bounded by the graph of y=2x 2 -3x+2, the x-axis, and the vertical lines x=0 and x=2.

7 If f is continuous on the closed interval [a,b], then there exists a number c in the closed interval [a,b] such that

8 If f is integrable on the closed interval [a,b], then the average value of f on the interval is

9 Find the average value of f(x)=3x 2 -2x on the interval [1,4]

10 At different altitudes in Earth’s atmosphere, sound travels at different speeds. The speed of sound s(x) (in meters per second) can be modeled by Where x is the altitude in kilometers. What is the average speed of sound over the interval [0,80]?

11  Read 4.4 Page 293 #11,13,15,19,23,27,33,39, 45,47

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