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Chapter 4: Q. 77 (page 363)
Hence Proved
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Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals.
Use a graph to check your answer.
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.
Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.
Fill in each of the blanks:
(a)
(b) is an antiderivative of .
(c) The derivative of is .
Prove part (b) of theorem 4.4 in the case when n is even: if n is a positive even integer, then
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