solve using given information

1. Evaluate the following integrals. a. /t2 cos(t3) dt 2_ b. [La 11:3ac+1 a c. / awn/a7 , as2 clue, where a is a positive constant. 0 2. A toy railroad car moves back and forth along a horizontal track for 5 seconds. There is a model train station positioned along the track. At the end of the 5 seconds, the car nishes up 5 cm to the right of the train station. The velocity function (in centimeters per second) of the railroad car is given by: v(t)= 3t212t-l9 forogtg3; 6t18 f0r3t5. At what time(s) does the car come to a rest? During what interva|(s) of time is the car moving to the right? During what interva|(s) of time is the car speeding up? What is the position of the car after 3 seconds, relative to where it started? What is the net displacement of the car between 1 second and 4 seconds? What is the total distance traveled by the car during the 5 seconds? Where was the car initially relative to the train station? When does the car reach its furthest position to the right, and at that instant of time, how far to the right of the train station is the car? P'QOthDP-Op'l\" i. How many times does the car pass the train station? j. Is the velocity function continuous at t = 3