Math205-Final-Fall-2015 - CONCORDIA UNIVERSITY Department...

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CONCORDIA UNIVERSITY Department of Mathematics & Statistics Course Number Sections Mathematics 205 All Examination Date Pages Final December 2015 2 Instructors: J. Brody, A. Daniels, T. Hughes Course Examiner U. Mgbemena A. Atoyan and H. Proppe Special Only approved calculators are allowed. Instructions: Show all your work for full marks. MARKS [10] 1. a. Sketch the graph of the function f ( x ) =
b. Use the Fundamental Theorem of Calculus to calculate the derivative of F ( x ) = x R - x 2 e 1 - t 2 d t , and determine whether F is increasing or decreasing at x = 1. [10] 2. Find the following indefinite integrals: ( a ) Z cos 3 ( x ) sin 2 ( x ) dx ( b ) Z ( e x + ln x ) dx [6] 3. Find F ( x ) such that F 0 ( x ) = x 2 + 4 x 2 - 4 and F ( - 1) = 0. [18] 4. Evaluate the following definite integrals (give the exact answers, do not approximate): ( a ) π/ 2 Z 0 cos( x ) 4 + sin 2 ( x ) dx ( b ) π/ 4 Z 0 sec 4 ( x ) dx ( c ) 3 Z 0 x 2 1 + x dx [8] 5.

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