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Chapter 4: Q. 12 (page 372)
Suppose f is a function whose derivative f' is given by the graph shown next. Use the given value of f, an area approximation, and the Fundamental Theorem to approximate the requested value.
Given that, approximate.
The approximated value is .
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Construct examples of the thing(s) described in the following. Try to find examples that are different than any in the reading.
(a) A function f for which the signed area between f and the x-axis on [0, 4] is zero, and a different function g for which the absolute area between g and the x-axis on [0, 4] is zero.
(b) A function f whose signed area on [0, 5] is less than its signed area on [0, 3].
(c) A function f whose average value on [−1, 6] is negative while its average rate of change on the same interval is positive.
Find the sum or quantity without completely expanding or calculating any sums.
Givenand, find.
Verify that. (Do not try to solve the integral from scratch.)
Fill in each of the blanks:
(a)
(b) is an antiderivative of role="math" localid="1648619282178"
(c) The derivative of is
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. (Hint for Exercise 54: ).
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