MATH 1242 FINAL EXAM Spring 2006 Part I (MULTIPLE CHOICE, NO CALCULATORS).

MATH 1242 FINAL EXAM Spring 2006 Part I (MULTIPLE CHOICE, NO CALCULATORS). 1. Compute R   3 2x + − 4 sin x dx. x 2 2 3 2x + − 4 sin x + C x 3 (b) 4x − 2 − 4 cos x + C x 2 (c) x3 + 3 ln |x| − 4 cos x + C 3 2 3 (d) x + 3 ln |x| + 4 cos x + C 3 2 (e) x3 + 3 ln |x| − 2 sin2 x + C 3 1 (a) 2  2. Compute 2 R1 −1 2 xex dx. (a) 2 (b) 2e (c) e 1 1 1 1 (d) e 3 − e− 3 2 2 (e) 0 3. Which of the following definite integrals gives the length of the curve y = sin x for 0 ≤ x ≤ π? Rπ√ (a) 0 1 + cos2 xdx Rπ (b) 0 cos xdx Rπ√ (c) 0 1 + cos xdx Rπ√ (d) 0 1 − cos xdx Rπ√ (e) 0 1 − cos2 xdx 1MATH 1242 FINAL EXAM Spring 2006 4. Complete the square in the denominator of the integrand of the following indefinite R 1 integral and then compute the integral dx. 2 x + 2x + 2 (a) 1 tan−1 (x + 1) + C 2 (b) ln |x2 + 2x + 2| + C (c) tan−1 (x2 + 2x + 2) + C 2 (d) (tan−1 x) + 1 + C (e) tan−1 (x + 1) + C 5. R1 0 xex dx = (a) e 1 2 (c) 2e (b) (d) 1 1 (e) e 2 6. Which of the following statements is correct? X∞ sin n X∞ 2n converges, and converges. 2 4 n=1 n n=1 n − 3 X∞ X∞ sin n 2n (b) diverges, and diverges. 2 4 n=1 n n=1 n − 3 X∞ sin n X∞ 2n converges, and diverges. (c) n=1 n2 n=1 n4 − 3 X∞ sin n X∞ 2n (d) diverges, and converges. n=1 n2 n=1 n4 − 3 X∞ sin n X∞ 2n4 (e) converges, and converges. n=1 n2 n=1 n4 − 3