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Chapter 4: Q. 44 (page 404)
Integral Formulas: Fill in the blanks to complete each of the following integration formulas.
The value of.
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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.
Write out all the integration formulas and rules that we know at this point.
Verify that(Do not try to solve the integral from scratch.
Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.
Your calculator should be able to approximate the area between a graph and the x-axis. Determine how to do this on your particular calculator, and then, in Exercises 21鈥�26, use the method to approximate the signed area between the graph of each function f and the x-axis on the given interval [a, b].
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