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Chapter 4: Q. 58 (page 327)
Given a simple proof that
We prove the statement
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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 [鈭�1, 6] is negative while its average rate of change on the same interval is positive.
Prove Theorem 4.13(b): For any real numbers a and b, we have. Use the proof of Theorem 4.13(a) as a guide.
Write out all the integration formulas and rules that we know at this point.
If and ,then find the values of each definite integral in Exercises . If there is not enough information, explain why.
.
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.
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