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Let $f$ be a continuous function defined on the interval $[2, \infty[$ such that $f(4)=14$, $|f(x)| < x^3+10$, and $$\int_4^\infty f(x)e^{-x/4} dx=-5\;.$$

Determine the value of: $$\int_4^\infty f\,'(x)e^{-x/4} dx\;.$$

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    Try integration by parts and use the fact that the given integral value to be $-5$ and $f(4)=14 ,|f(x)| < x^3+10$, then you should get $\frac{14}{e}$ as your answer2012-03-18
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    @Kirthi: I think it should be $-\frac{14}{e}-\frac{5}{4}$.2012-03-18
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    I think it is rather $\frac{14}{e} + \frac{5}{4}$2012-03-18
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    You need to assume more than just continuity here. To use integration by parts (or the Fundamental Theorem of Calculus), you want $f(x)$ to be absolutely continuous.2012-03-18

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