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Given: $f^{\prime\prime}(x)$ is continuous, $f(\pi) = 0$, and $$\int_0^\pi (f(x)+f^{\prime\prime}(x))\sin(x) \, dx = 2.$$

Find: $f(0)$.

I know integration by parts etc, but I do not know which particular concept(s) I'm supposed to apply for this one. Or is there a specific theorem I am missing?

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    I've formatted your question. Please make sure that I haven't changed your intended meaning. Also, if you are interested in learning how these things are written, you can click "edit" to see the code I typed.2012-04-29
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    You could try applying integration by parts twice to $\int_0^{\pi}f''(x)\sin x\,dx$.2012-04-29
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    This looks like an exercise in applying the knowledge creatively to produce information that could be useful. You are not expected to **know** what to do. Instead, you're expected to conjecture and experiment until you find something that is useful.2012-04-29

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