Calculus :

1. I have tried 19.36, 20.16, and 20.17 as answers

EXAMPLE 7 A particle moves along a line so that its velocity at time t is v(t) = t - t - 20 (measured in meters per second). (a) Find the displacement of the particle during 3 S t s 6. (b) Find the distance traveled during this time period. SOLUTION (a) By this equation, the displacement is s (6) - 5(3) = / v(t ) at -13 ( 12 - t - 20 ) at 76 12 2 - 20t 13 -10.5 This means that the particle's position at time t = 6 is 10.50 meters to the left of its position at the start of the time period. (b) Note that v(t) = t2 - t - 20 = (t - 5)(t + 4) and so v(t) s @ . 0 on the interval [3, 5] and v(t) > @ . 0 on [5, 6]. Thus, from this equation, the distance traveled is 12 ( -2 + + + 20 ) at + 15 (2 - + - 20 ) at + + 20t + NT - 20t Co/ 20 X m.The graph of fis shown. Evaluate each integral by interpreting it in terms of areas. 3' y=n Evaluate the integral by making the given substitution. (Use C for the constant of integration.) [x3(5+x4)4dx, u=5+x4 Z Need Help? Evaluate the integral by making the given substitution. (Use C for the constant of integration.) [X2'/X3+ 19 dx, u=x3+19 Z Need Help? ___