math205 mid2.pdf - CONCORDIA UNIVERSITY Course Mathematics...

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CONCORDIA UNIVERSITYDepartment of Mathematics & StatisticsCourseNumberSectionsMathematics205AllExaminationDateDurationMidterm5 March, 20171 h 30 minSpecialOnly approved calculators are allowedInstructions:Show all your work for full marks1. (10 marks):(a)Graph the functionf(x) =-4-x2-2x2|x-3| -1x >2on the interval [-2,6],and use it to calculate the definite integral6R-2f(x) dxin terms of area.(b)Use the Fundamental Theorem of Calculus to find the functionf(x) andthe constantAsuch that2Rxf(t)dt=x-x2+A.2. (6 marks):Find the antiderivativeF(t) off(t) = (sec4t+ 1) such thatF(0) = 0.3. (10 marks):Calculate the following indefinite integrals(a)Zexe2x-ex-2dx(b)Zx5x3-4dx4. (12 marks):Evaluate the following definite integrals (do not approximate):(a)

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