1. Let f be a continuous function on the closed interval [0,1]. Which of the following statements about f must be true?1. Let f be a continuous function on the closed interval [0,1]. Which of the following statements about f must be true?
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A. None |
B. I only |
C. II only |
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D. III only |
E. The correct answer is not given by A, B, C, or D. |
Solution: The answer is C
Let f(x) = x/2. Then I and III are not true, for
Statement II is true.
Reason: Let r = x/2, then dx = 2dr. By substitution,
Note: The definite integral is a number that does not depend on x. Therefore, any letter can replace x.