29. At time t in seconds, your velocity v in meters/second is given by v(t) = 8 + t2 for 0 ? t ? 6. Use ?t = 2 to estimate the distance traveled during this time. Find the upper and lower estimates, and then average the two.

39. Find the antiderivative F (x) for f (x) = 2 sin(x) that satisfies the property F (0) = 0

40. Find the antiderivative F(x) for f(x) = 13(x) that satisfies the property F(0) = 3

41. Find the antiderivative F (x) for f (x) = x4 + 4x that satisfies the property f (5) = 10

36. Let S, f(x)dx = 6 and S, g(x)dx = 2. Find the following. (a) S2 (f(2) + g(x)) dac (b) S2 (f (20) - g(2) ) dac (c) Ng(x -2) da (d) f2 -89(x) da (e) S2 (3f(x) - 49(x)) dac (f) S' f (x) doc (g) Mg(x) dx 37. Find these indefinite integrals: (a) S(18+223 + - + 2 (b) S(7 sin(x) + 4 cos(2) + e2" + 2") dx ( c ) S( vat ( Vx) 5) dx 38. Consider the function f(x) = x2 + 2x + 3 (a) Calculate fo f(x)dx34. The figure below shows the amount of electrical current I(t), measured in coulombs per second, flowing through a wire t seconds after a switch is flipped. 10 I (t ) 8 6 4 2 N (a) Estimate I(t) at using a right Riemann sum with 4 subdivisions, (b) Interpret I(t) dt in the context of this question. Make sure to write your answer in a complete sentence with units