18. • Sf² f(x) f(x) dx = 5, • [f(x) dx f(x) dx = 7, •f*9(x) dx g(x) dx-3, and • L² 9(x g(x) dx = 5. Use these values to evaluate the given definite inte S² (f(x) + g(x)) dx 19. امل (f(x) - g(x)) dx 20. ² (3f(x)+2g(x)) dx 21. Find values for a and b such that ² (af(x) + bg(x)) dx = 0 208 In Exercises 10-13, a graph of a function f(x) is given; the numbers inside the shaded regions give the area of that re- gion. Evaluate the definite integrals using this area informa- tion. 10. V-x) 13. 2 05- (a) (b) [f(x)dx [F(x) dx (c) [f(x) dx (d) -3f(x) dx (a) [sx dx (b) (x² + 3) de In Exercises 14-15, a grap ject moving in a straight li based on that graph. 2 11. 4/1 1 3 12. 2) 14. - (a) [f(x) dx (b) [f(x) dx (c) [[f(x) dx (d) [f(x) dx (a) What is the objec (b) What is the objec (c) What is the objec 54-3-3 -5 (a) f(x) dx (c) f(x) dx (b) [f(x) dx (d) [f(x) dx 15. (a) What is the object (b) What is the objec (c) What is the objec 16. An object is thrown stra by v(t) -32r+64, of 48 feet. (a) What is the objec (b) What is the objec (c) When does the m (d) When will the obj when the displace function f(x) is given; the ls s give the area of that re- using this area informa- 13.2 (c) f(x) dx (d) -3f(x) dx (a) * 5x dx 3/3 (c) ((x-1)³ dx (d)((x-2)²+5) dx (b) f (x²+3) dx In Exercises 14-15, a graph of the velocity function of an ob- ject moving in a straight line is given. Answer the questions based on that graph. 14. (c) [f(x) dx (0) f(x) dx -1 (a) What is the object's maximum velocity? (b) What is the object's maximum displacement? (c) What is the object's total displacement on [0,3]? (c) f(x) dx (d) f(x) dx 15. 2 1 B (a) What is the object's maximum velocity? (b) What is the object's maximum displacement? (c) What is the object's total displacement on [0.5]? 16. An object is thrown straight up with a velocity, in ft/s, given by v(t)=-32t+64, where t is in seconds, from a height of 48 feet. (a) What is the object's maximum velocity? (b) What is the object's maximum displacement? (c) When does the maximum displacement occur? (d) When will the object reach a height of 0? (Hint: find when the displacement is -48ft.) Problems In Exercises 5-9, a graph of a function f(x) is given. Using the geometry of the graph, evaluate the definite integrals. 5. 6. 2 y= -2x+4 2 1 -1 (a) (-2x+4) dx (d) (-2x+4) dx ( (b) (-2x+4) dx (e) (-2x+4) d -2x+4) dx ( (c) -2x+4) dx (f) (-6x+12) dx 1 2 4 -1 y-f(x) (a) f(x) dx (d) f(x) dx (b) f(x) dx (e) f(x) dx (c) f(x) dx (f) -2f(x) dx 3 2 9. 1 ( (b) f(x) dx (e) (2x-4) dx * te) | 25(*) dx r)」(4—8) (4x-8) dx 2 y-x-1 少 8. 1 9. 1 (a) *(x-1) dx (d) (x-1) dx (b) (x-1) dx (c) L(x- (e) e) √(x-1) dx (x-1) dx (f) * ((x − 1) + 1) dx 10x)- (4-(x-2) 2 1 (a) f(x) dx [f(x) dx (b) [f(x) dx (d)*5f(x) dx 207