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We are asked to evaluate: [ \int_{0}^{1} \left( 2x \sin \frac{1}{x} - \cos \frac{1}{x} \right) dx ] using the Fundamental Theorem of Calculus. Notice that the derivative of (\sin \frac{1}{x}) is: [ \frac{d}{dx} \left( \sin \frac{1}{x} \right) = \cos \frac{1}{x} \cdot _________ ___ ________ ____ ______ ______ _________.
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