Part 1: True and False: Indicate whether the following statements are true (T) or false (F). (1 mark each) Assume that f is a continuous function and that F is any antiderivative of f. Then fo f(t) dt = F(b) - F(a). 2. [', f(x) dx = 0 if f(x) is an even function. 3. [, f(x) dx = 0 if f(x) is an odd function. All continuous functions have antiderivatives. 5. All continuous functions have derivatives. 2 6. A continuous function can have only one antiderivative. 7. Hey de = arctan(r) + C 8. The Change of Variables formula shows that if u = g(t), then f f(o(t))g'(t) at = [ f(u) du. 9. To check whether the general indefinite integral that you calculated is correct, simply take its derivative and determine if you end up with the integrand with which you started. 10. If F(x) is the antiderivative of f(z), then F(x) = f(x). 11. The Fundamental Theorem of Calculus Part 1 provides us with a rule for differentiating integral functions. 12 The Fundamental Theorem of Calculus Part 2 provides us with a tool for evaluating integrals. 13. The Fundamental Theorem of Calculus shows that differentiation and integration can be thought of as inverse processes. 14. The indefinite integral J f(x) dr represents a family of functions that are the antiderivatives of f(I). 15. The definite integral J. f(x) da produces a number that is defined as a limit of Riemann sums. 16 The definite integral f. f(x) dr produces a number that represents the net area between f(x) and the x-axis over a specified interval when a