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Chapter 4: Q. 13 (page 404)
Calculating definite integrals with limits of Riemann sums: Calculate
the exact value of each the following definite integrals by
setting up a general Riemann sum and then taking the limit
as n鈫掆垶.
The exact value is 24 .
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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.
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.
Suppose f is a function whose average value on
is and whose average rate of change on
the same interval is . Sketch a possible graph for f .
Illustrate the average value and the average rate of change
on your graph of f.
Describe the intervals on which the function f is positive, negative, increasing and decreasing. Them describe the intervals on which the function A is positive , negative, increasing and decreasing
Write out all the integration formulas and rules that we know at this point.
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