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Chapter 4: Q. 2 TB (page 361)
State the definition of the definite integral of a function f on an interval
The definition of the definite integral of a function f on an interval is following.
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Use integration formulas to solve each integral in Exercises 21鈥�62. You may have to use algebra, educated guess- and- check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. Check each of your answers by differentiating. (Hint for Exercise 54: ).
Calculate the exact value of each definite integral in Exercises 47鈥�52 by using properties of definite integrals and the formulas in Theorem 4.13.
Explain why we call the collection of antiderivatives of a function f a family. How are the antiderivatives of a function related?
Suppose f is a function whose average value on is
and whose average rate of change on the same in-
terval is . Sketch a possible graph for f . Illustrate the
average value and the average rate of change on your
graph of f .
Determine which of the limit of sums in Exercises 47鈥�52 are infinite and which are finite. For each limit of sums that is finite, compute its value
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