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Unformatted text preview: c Kendra Kilmer April 2, 2009 Section 6.1 - Antiderivatives and Indefinite Integrals
Example 1: What are the possible functions whose derivative is x? Definition: The General Antiderivative of f (x) on an interval is F(x) + C, where C is any real number constant, if Also written as which is known as the indefinite integral of f , where F (x) = f (x) Note: Antidifferentiation (or integration) is the inverse operation of Rules of Integration: 1. xn dx = . 2. k dx = 3. ex dx = 1 dx = x [ f (x) g(x)] dx = 4. 5. 6. [k f (x)] dx = 1 c Kendra Kilmer April 2, 2009 Example 2: Find the following: a) 8 dx b) x5 dx c) 1 4 x dx 3 d) 2 dt t9 e) (5x4 + x3 - 2) dx f) 3 dx x g) (ex + x3 ) dx h) 3 1 (3 x - 2 - x 2 ) dx x i) 4x2 + x3 dx 8x j) (x - 2)(x + 3) dx 2 c Kendra Kilmer April 2, 2009 Example 3: Find y if y(1) = 1 and dy 3 1 = + dx x x2 Example 4: The daily marginal revenue function for the Black Day Sunglasses Company is given by MR(x) = 30 - 0.0003x2 for 0 x 540, where x represents the number of sunglasses produced and sold. a) Knowing that R(50) = 1487.50, find the revenue function. b) Find the price demand function for the sunglasses. c) What will the price be when the demand is 250 sunglasses? Section 6.1 Suggested Homework Problems: 1,19,25,31,43,49,55,61,67,73,79,83,89,95,97,107 and supplemental problems 3 ...
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