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Chapter 4: Q. 48 (page 404)
Integral Formulas: Fill in the blanks to complete each of the
following integration formulas.
(The last six formulas involve hyperbolic functions and their inverses.)
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If , and , then find the values of each definite integral in Exercises . If there is not enough information, explain why.
Use the graph of f to estimate the values of A(1), A(2), A(3)
Write each expression in Exercises 41鈥�43 in one sigma notation (with some extra terms added to or subtracted from the sum, as necessary).
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 .
For each function f and interval [a, b] in Exercises 27鈥�33, use the given approximation method to approximate the signed area between the graph of f and the x-axis on [a, b]. Determine whether each of your approximations is likely to be an over-approximation or an under-approximation of the actual area.
left sum with
a) n = 3 b) n = 6
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