009B Sample Final 2, Problem 1

(a) State both parts of the Fundamental Theorem of Calculus.

(b) Evaluate the integral

$\int _{0}^{1}{\frac {d}{dx}}{\bigg (}e^{\tan ^{-1}(x)}{\bigg )}dx$

(c) Compute

${\frac {d}{dx}}\int _{1}^{\frac {1}{x}}\sin t~dt$

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Solution

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