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3. Formulate an analogous statement on integrability on (a, b) under the assumptions of integrability of ƒ on intervals (u, b) where u € (a, b). Analogously, prove the statement formulated in Q3.

3. Formulate an analogous statement on integrability on (a, b) under the assumptions of integrability of ƒ on intervals (u, b) where u € (a, b). Analogously, prove the statement formulated in Q3.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Theorem. Let -∞ ≤ a < b ≤ ∞. Suppose that function ƒ is integrable on the interval (a, v) for all v € (a, b). Then ƒ is integrable on the interval (a, b) if and only if there exists M <∞ such that Vv € (a, b). V [13 Additionally, if this condition holds then ['s a (If b \f|<M, f = lim v→b- •V a fƒ. = ∞ we understand lim→ to be lim₂→∞). (1) 3. Formulate an analogous statement on integrability on (a, b) under the assumptions of integrability of f on intervals (u, b) where u € (a, b). Analogously, prove the statement formulated in Q3.
Transcribed Image Text:Theorem. Let -∞ ≤ a < b ≤ ∞. Suppose that function ƒ is integrable on the interval (a, v) for all v € (a, b). Then ƒ is integrable on the interval (a, b) if and only if there exists M <∞ such that Vv € (a, b). V [13 Additionally, if this condition holds then ['s a (If b \f|<M, f = lim v→b- •V a fƒ. = ∞ we understand lim→ to be lim₂→∞). (1) 3. Formulate an analogous statement on integrability on (a, b) under the assumptions of integrability of f on intervals (u, b) where u € (a, b). Analogously, prove the statement formulated in Q3.
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