Integral, Continuity and Limits
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Q:
Suppose and are continuous and F(x) =
Let
(a) prove that f'(x) + g'(x) =0 for all x
(b) Prove that f(x) + g(x) = /4 for all x. Deduce that
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Suppose and are continuous and F(x) =
Let
(a) prove that f'(x) + g'(x) =0 for all x
Prove that f(x) + g(x) = /4 for all x. Deduce that
Solution:
(a) We will apply the formula of Leibniz for derivative of an integral with parameters:
( 1)
For f(x), we will have:
( 2)
where
...
Solution Summary
The Leibniz derivative and the Poisson integral are applied. The solution is detailed and well presented.
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