4. Suppose that f and g are Riemann integrable functions on [a, b]. (a) Show that 1/2 1/2 || f(x)g(x) dx| < | f°(x) dx3| 8*(x) dx This is the Schwarz inequality for integrals. [Hint: For a, ß, real numbers, S (af (x) – Bg(x))* dx>0.]

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Q: Let f,g:[a, b]-R are Riemann integrable , f-g is Riemann integrable. صواب İhi

A: True Statement  Detailed Explanation :-

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A: This is a problem of measure theory.

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A: According to the given data, prove the following statement:

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Q: Let f,g:[a, b]-R are Riemann integrable , f-g is Riemann integrable. صواب İhi

A: We know that

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A: Solution:-

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A: We have to check

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A: See the solution below.

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A: I have proved limiting value is equal to functional value

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A: We have to prove that following identity.

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A: let f be Riemann integral an [a, b] then clearly f is bounded.