advertisement

Math 105 Integration Questions from recent finals Richard Anstee 2016 This list may grow over time. For the stated definite or indefinite integrals determne the answer. 1. Given f 0 (1) = 2 and f 0 (2) = 3, determine Z 2 f 0 (x)f 00 (x)dx 1 2. 3. Z Z cos−1 (x)dx cos3 (x) sin4 (x)dx 4. Z √ 5. dx 3 − 2x − x2 x − 13 dx −x−6 Z x2 6. Determine k so that Z 1 (1 + k|x|)dx = 1 −1 7. Z 5/2 dx √ 25 − x2 0 8. Z 2 |2x| dx −1 9. Compute F 0 (π) given F (x) = Z cos(x) 0 t3 1 dt +6 10. Compute the area bounded by the curve y = f (x) and the x-axis and between x = 0 and x = 1. 1 f (x) = (2x − 4)2 11. Z ln(x) dx x7 12. (this was a 6 mark question). You are given f (0) = 1, f (2) = 3, and f 0 (2) = 4. Determine Z 4 0 √ f 00 ( x)dx