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Chapter 4: Q. 37 (page 405)
The average value of the function on
The average value ofis
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Write each expression in Exercises 41–43 in one sigma notation (with some extra terms added to or subtracted from the sum, as necessary).
Calculate the exact value of each definite integral in Exercises 47–52 by using properties of definite integrals and the formulas in Theorem 4.13.
Consider the region between f and g on [0, 4] as in the
graph next at the left. (a) Draw the rectangles of the left-
sum approximation for the area of this region, with n = 8.
Then (b) express the area of the region with definite
integrals that do not involve absolute values.
Shade in the regions between the two functions shown here on the intervals (a) [−2, 3]; (b) [−1, 2]; and (c) [1, 3]. Which of these regions has the largest area? The smallest?
Use integration formulas to solve each integral in Exercises 21–62. 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.
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