47. Define F(x) by F(x) = (t3 + 1) dt (a) Use Part 2 of the Fundamental Theorem of Calculus (b) Check the result in part (a) by first integrating and then to find F'(x). differentiating. 49-54 Use Part 2 of the Fundamental Theorem of Calculus and (where necessary) Formula (18) of Section 5.10 to find the derivatives. 49. e" dt 50. dt dx LJo cos t2 51. It - 1l dt 52. cos Vt dit dx LJo dx dx L2 1+13 55. State the two parts of the Fundamental Theorem of Calcu lus, and explain what is meant by the statement "Differer tiation and integration are inverse processes." 67-70 A particle moves along an s-axis. Use the given info mation to find the position function of the particle. 67, y(t) = ts_ 2t2 + 1 ; s(0) = 1