Homework 9 MATH 2413 - Calculus I Complete all work neatly on your own paper and not on this assignment sheet itself. All steps should be shown and your work must be easily readable. Problems without work or explanation will receive no credit. You will be turning in all homework online through DZL. Antiderivatives Find the indefinite integral and check the results by differentiation. 1. [ ( x+ 3 ) dx 2. [ ( 2.x - 3.12 ) dx 10. dt 3. [ ( 13 + 2) dx 11. [ (2sin.x + 3cos.x) dx 4. [ (.1/ + 2x+ 1) dx 12. (1-cset cott) dt 5 . [Vridx 13. [ (sec- 0 -sine) de 6. J - dx 14 . [10e'dt 7 . +x +1 15. [(8-2ex - sin.x) dx 2 - 2 8. [ (1 + 1) (3.x - 2) dx Solve each of the following initial value problems. 16 . f' (x) = 4x, f (0) = 6 18 . 8 " ( x ) = 1 , 8' (0 ) = 6 , 8 (0 ) = 3 17. h' (t) = sint, (0, 2) 19. A particle moves alone the x-axis at a velocity of v(t) = -, 1 > 0 . At time / =1, its position is x = 4 . Find the acceleration and position functions for this particle. 20. A particle, initially at rest, moves along the x-axis such that its acceleration at time t > 0 is given by a (t) = cos(t) . A the time t = 0its position is .x = 3. a. Find the velocity and position functions for the particle. b. Find the values of t for which the particle is at rest