8. Esxpress the following integral as a limit of Riemann sums and then calculate the resulting limit (2- 2)dz Answer: 9. (10 points) A particle moves an acceleration function a(t)-5 + 4t-2t2 m/s. Its initial velocity is r(0) = 3 nn/s, and its initial position is s(0) 10 m. Find the position function s(t). Answer: s(t) t3-6t4 + 3t 10. The speed of a car traveling due east is recorded in Tablel. Table 1: Speed of a car time t minutes 10 20 30 40 5060 velocity v mph (a) Estimate (t) dt by Lo, where t is measured in hours. (b) Estimate , u(t) dt by R6, where t is measured in hours. (t) dt, where t is measured in hours. 45 (e) Assuming o() is monotonic in between recorded measurements, determine upper and lower bounds for Answers: (a) 155/6 miles (b) 95/3 miles (c) 21.5 s /v(t) dt 36 1. (0 painto) Calenlabet cos(t2) dt. Answer: 3r2 cos(z") 12. Differentiate (a) / tan(t2)dt Ansuer: 3r' tan(H)-tan(H) sec(t3) dt Answer: cos(zx) sec(sin(x)) +sin(x) sec(cos(x)) cos(a)