MATH1014 Calculus II
Each of the following MC questions is worth 3 points. No partial credit. 1. What is the colour version of your exam paper? (Read the top left corner of the cover page!) Make sure that you have also written and marked your ID number correctly in the I.D. No. Box in the MC answer sheet. If you do not do both correctly, you lose the points of this question. (a) Green (b) Orange (c) White (d) Yellow (e) Sample 2. Evaluate the integral Z 1 0 4 cos(2πx) sin2 (πx)dx. (a) −2 (b) −1 (c) 1 (d) 2 (e) 4 3. Evaluate the improper integral Z 2 0 4x √ 4 − x 2 dx. (a) 2 (b) 4 (c) 6 (d) 8 (e) 10 2 4. Evaluate the improper integral Z ∞ 0 2x (x 2 + 1)2 dx. (a) 1 (b) 2 (c) 3 (d) 4 (e) divergent 5. Find the area enclosed by the curves y = x + 1, y = 2 (x + 1)(x + 2) and x = 4. 1 2 3 4 5 1 2 3 4 5 6 x y (a) ln 3 5 + 12 (b) ln 2 5 + 12 (c) 2 ln 3 5 + 12 (d) 2 ln 2 5 + 12 (e) 3 ln 3 5 + 6 6. The graph of the function y = 3 + x 2 over the interval 0 ≤ x ≤ √ 12 is rotated about the y-axis to generate a surface of revolution. Find the area of the surface. (a) 63π (b) 57π (c) 42π (d) 35π (e) 26π
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