Unformatted text preview: f ( x ) is f ( x ) = e xcos x +3 sin x + x 2 + C . Since f (0) = 11 + 0 + C = C = 2, we have C = 2, so the particular solution is f ( x ) = e xcos x + 3 sin x + x 2 + 2 . In physics, antidiﬀerentiation is useful to recover the position function from a given velocity function or acceleration function. Example 3. A particle moves in a straight line with constant acceleration 32 ft/s 2 . Its initial velocity is 60 ft/s and its initial displacement is 100 ft. Find its position function s ( t ). Solution Since s 00 ( t ) =32, s ( t ) =32 t + C 1 and s ( t ) =16 t 2 + C 1 t + C 2 . We know that v (0) = s (0) = 60, and it gives C 1 = 60. We also have a (0) = s 00 (0) = 100, hence C 2 = 100. Therefore, s ( t ) =16 t 2 + 60 t + 100. 1...
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 Fall '09
 BenedictGross
 Calculus, Antiderivatives, Derivative, position function

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