Proving Lagrange's Remainder from Taylor's Theorem

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Homework Statement


I'm interested in the use of the mean value theorem of integration to convert Taylor's theorem into Lagrange's remainder. Though, I'm confused as to how it's used in the conversion. Could someone explain to me how the MVT of integration is used to convert Taylor's theorem into Lagrange's remainder?


Homework Equations


I"m bad with LaTeX, but it's Taylor's theorem right here: http://upload.wikimedia.org/math/6/d/7/6d70410a12402233d48598420cb7995f.png
and Lagrange's remainder right here: http://upload.wikimedia.org/math/2/1/2/212f9b5c042521027f93d959faf79798.png

The Attempt at a Solution


I reviewed the mean value theorem for integration, but I'm rather clueless as to how it's used to convert Taylor's theorem into Lagrange's remainder.
 

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