MATH 181 Study Guide - Final Guide: Antiderivative, 4Dx
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Problem 1 solution: the graph of a function g(x) is given below. Let g be an antiderivative for g on the interval [0, 5] with g(1) = 2. Solution: since g is an antiderivative of g we know that g (x) = g(x). G(x) = ! g(x) dx where g(x) = x 1 if 0 x < 3 if 3 x < 4. 2x + 10 if 4 x 5. 2: on the interval 0 x < 3, we have g(x) = x 1. The value of c1 is found by using the fact that g(1) = 2. G(1) = 2 (1)2 1 + c1 = 2. Therefore, on the interval 0 x < 3 we have g(x) = 1: on the interval 3 x < 4, we have g(x) = 2. The value of c2 is found by ensuring continuity of g(x) at x = 3. G(x) x 3 % 1 lim x2 x +