For each of the questions below, indicate if the statement is true (T) or false (F). (a) A continuous function on an open interval is integrable. True False (b) A continuous function on a closed interval is integrable. True False (c) If f(x) is continuous on a closed interval [a, b] and f f(x)dx ≥ 0, then f(x) > 0 for some x True False

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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For each of the questions below, indicate if the statement is true (T) or false (F).
(a) A continuous function on an open interval is integrable.
True
False
(b) A continuous function on a closed interval is integrable.
True
False
(c) If f(x) is continuous on a closed interval [a, b] and ſå f(x)dx ≥ 0, then ƒ(x) ≥ 0 for some x € [a, b].
True
False
(d) If f(x) and g(x) are integrable on [a, b] and g(x) ≤ f(x) for all x € [a, b], then f g(x)dx ≤ f f(x)dx .
True
False
(e) Every continuous function has an antiderivative.
True
False
Transcribed Image Text:For each of the questions below, indicate if the statement is true (T) or false (F). (a) A continuous function on an open interval is integrable. True False (b) A continuous function on a closed interval is integrable. True False (c) If f(x) is continuous on a closed interval [a, b] and ſå f(x)dx ≥ 0, then ƒ(x) ≥ 0 for some x € [a, b]. True False (d) If f(x) and g(x) are integrable on [a, b] and g(x) ≤ f(x) for all x € [a, b], then f g(x)dx ≤ f f(x)dx . True False (e) Every continuous function has an antiderivative. True False
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