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WZ
Numerade Educator

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Problem 70 Hard Difficulty

If $ f(0) = g(0) = 0 $ and $ f^n $ and $ g^n $ are continuous, show that
$$ \int_0^a f(x) g^{\prime\prime} (x) dx = f(a)g^\prime(a) - f^\prime(a)g(a) + \int_0^a f^{\prime\prime} (x) g(x) dx $$

Answer

$f(a) g^{\prime}(a)-f^{\prime}(a) g(a)+\int_{0}^{a} f^{\prime \prime} g d x$

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Video Transcript

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