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**4.4 The Fundamental Theorem of Calculus**

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**Evaluating a Definite Integral**

Evaluate each definite integral.

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**A definite integral involving absolute value**

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**Using the fundamental theorem to find area**

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

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**Using Mean Value Theorem**

Find the values of c guaranteed by the mean value theorem for integrals over the given interval.

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**Finding the Average Value of a Function**

Find the average value of on the interval [1,4].

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**The Definite Integral as a Function**

Evaluate the function at

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**Using the Second Fundamental Theorem of Calculus**

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**Using the Second Fundamental Theorem of Calculus**

Find the derivative of

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