can anyone tell me how to prove the 1st mean-value theorem for integral(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\int^{b}_{a}f(x)g(x)dx=f(\xi)\int^{b}_{a}g(x)dx[/tex]

by applying Lagrange mean-value theorem to an integral with variable upper limit?

thanks a lot.

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# Alternative proof for the 1st mean-value theorem for integrals

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