Math 115 Winter 2017, Written Assignment 4 Due by Wednesday, March 29, 5 p.m. For Questions 1-4, determine if the integral converges or diverges. Evaluate those that converge. Z 9 3 1. 1 Z 2. 0 Z 1 ln x dx. x 3. 0 Z 1 dx. x9 4. ex dx. e2x + 3 e|x| dx. Z 5. Use the comparison theorem to determine whether 0 diverges. 3 tan1 x dx converges or 2 + ex 1 6. Find the length of the curve x = 13 y 2 y 2 , 1 y 9. x5 1 + , 1 x 2. 6 10x3 Z xp 8. Find the length of the curve y = 3t4 1 dt, 2 x 1. 7. Find the length of the curve y = 2 9. The graph of the curve y 3 = x2 is given below. y 0 x (a) Find the arc length of the curve from the point (0, 0) to (1, 1) by integrating with respect to x. Note that it is an improper integral. (b) Find the arc length of the curve from the point (0, 0) to (1, 1) by integrating with respect to y. 10. Evaluate the integrals. Z dx (a) 2 x4+x Z (b) x2 2x 1 dx (x 1)2 (x2 + 1)