3 where is an antiderivative of f. Two-step approach for using FTC I to evaluate the definite integral Compute - Evaluate f(x)dx = F(x) + C. f(x) dx = F(x) = F(b) - F(a). b f(x)dx: Antiderivative formulas are helpful for evaluating definite integrals. See the summary in Section 5.3 and the table of integrals in this text's endleaf. WHITE 300 "x5" EXERCISES initary Questions Suppose that F'(x) = f(x) and F(0)=3, F(2) = 7. What is the area under y = f(x) over [0,2] if f(x) ≥ 0? What is the graphical interpretation of F(2) F(0) if f(x) takes on positive and negative values? Suppose that f is a negative function with antiderivative F such that 7 and F(3)=4. What is the area (a positive number) between the is and the graph of ƒ over [1,3]? ercises Exercises 1-4, sketch the region under the graph of the function and ind its area using FTC I - [0,1] 1 = [1,2] 3. Are the following statements true or false? Explain. (a) FTC I is valid only for positive functions. (b) To use FTC I, you have to choose the right antiderivative. (c) If you cannot find an antiderivative of f, then the definite integral does not exist. 4. Evaluate ef f'(x)dx, where ƒ is differentiable and f(2) = f(9)=4. 7. (4x-9x²) dx 8. u² du 2. f(x)=2x-x², [0,2] 9. (12x³ +3x²-4x)dx 10. (10x+3x5) dx 4. f(x)=cosx, [0,4] 11 21³-61³) dr 12. 6. 2 2dx 13. √ydy Exercises 5-40, evaluate the integral using FTC 1. 5. Idx 14. L • (5u4 x4/3 dx en th a REV6