5.4.11-eg-1 - To this end let F ( u ) = Z u 5 t 2 / 3 dt,...

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Example Find F 0 ( x ) if F ( x ) = Z x 3 5 t 2 / 3 dt. Solution: We cannot directly appeal to the first part of the Fundamental Theorem of Calculus because the upper limit of the definite integral is not x alone. However, we can still find F 0 ( x ) by making use of the Chain Rule.
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Unformatted text preview: To this end let F ( u ) = Z u 5 t 2 / 3 dt, where u = x 3 . Then, dF dx = dF du u = x 3 du dx = u 2 / 3 u = x 3 3 x 2 = x 3 2 / 3 3 x 2 = x 2 3 x 2 = 3 x 4 ....
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This note was uploaded on 04/02/2012 for the course MTH 132 taught by Professor Kihyunhyun during the Fall '10 term at Michigan State University.

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