solution_c7pdf - armington(kma786 5.5 Stepp(55860 This...

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armington (kma786) – 5.5 – Stepp – (55860) 1 This print-out should have 7 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0points Find the value of I = integraldisplay π/ 2 0 4 sin 2 t dt . 1. I = 3 2. I = 5 3. I = 4 correct 4. I = 7 2 5. I = 9 2 Explanation: Set u = 2 t . Then du = 2 dt , while t = 0 = u = 0 , and t = π 2 = u = π . In this case, I = 1 2 integraldisplay π 0 4 sin u du = 1 2 bracketleftBig - 4 cos u bracketrightBig π 0 . Now cos 0 = 0 , cos π = - 1 . Consequently, I = 2 parenleftBig - ( - 1) - ( - 1) parenrightBig = 4 . keywords: IntSubst, IntSubstExam, 002 10.0points Evaluate the integral I = integraldisplay 1 0 4 x (1 - x 2 ) 5 dx . 1. I = - 4 5 2. I = 2 5 3. I = 1 3 correct 4. I = - 2 3 5. I = - 1 3 6. I = 2 3 Explanation: Set u = 1 - x 2 . Then du = - 2 x dx while x = 0 = u = 1 , x = 1 = u = 0 . In this case, I = - 2 integraldisplay 0 1 u 5 du = 2 integraldisplay 1 0 u 5 du . Consequently, I = 2 bracketleftBig 1 6 u 6 bracketrightBig 1 0 = 1 3 . 003 10.0points The graph of f has slope df dx = x radicalbig 2 x 2 + 1 and passes through the point (2 , 4). Find the y -intercept of this graph.
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