Section 3.1: (page 175) Numbers 15-19 all, 27-29 all, 34-41 all Section 3.2: (page 187) Numbers 1-5 all Section 3.3: (page 194) Numbers 1-19 odd Section 3.4: (page 200) Numbers 1, 2, 4-12 all

textbroker.com X Final Exam X X Canvas LMS X MATH140-12141 (ONL) X BusCalc.pdf X *Dashboard X -> C A Not Secure | opentextbookstore.com/buscalc/BusCalc.pdf Update : Suggested Sites M Gmail YouTube Disney+ canvas find cards saved o... Other Bookmarks BusCalc.pdf 178 / 272 69% + 174 14. What are the units for the "area" of a rectangle with the given base and height units? Base units Height units "Area" units miles per second seconds hours dollars per hour square feet feet kilowatts hours houses people per house meals meals In problems 15-17, represent the area of each bounded region as a definite integral, and use geometry to determine the value of the definite integral. 15. The region bounded by y = 2x , the x-axis, the line x = 1, and x = 3. 175 16. The region bounded by y = 4-2x, the x-axis, and the y-axis. 17. The shaded region in the graph to the right. y = 3 - 2 176 Chapter 3 The Integral Business Calculus 178 area = 5 18. Using the graph of f shown and the given areas of area = 2 several regions, evaluate (a) Jf(x) dx ( b) f f ( x) dx ( c ) f f ( x ) dx 0 3 5 area = 3 19. Using the graph of f shown and the given areas of several regions, evaluate: (a) J g(x) dx b) J g(x) dx area = 6 3 177 8 (c) J g(x) dx (d) J g(x) dx area 20. Use the graph to evaluate: (a) h(x) dx (b) S h(x) dx -2 4 c J h(x) dx (d) J h(x) dx -2 -2 178 21. Your velocity along a straight road is shown to the right.textbroker.com X Final Exam X X Canvas LMS X MATH140-12141 (ONL) X BusCalc.pdf X *Dashboard X -> C A Not Secure | opentextbookstore.com/buscalc/BusCalc.pdf Update : Suggested Sites M Gmail YouTube Disney+ canvas find cards saved o... Other Bookmarks BusCalc.pdf 179 / 272 69% 175 Chapter 3 The Integral Business Calculus 179 b In problems 23 - 26, the units are given for x and for f(x) . Give the units of J f(x) dx . 176 23. x is time in "seconds", and f(x) is velocity in "meters per second." 24. x is time in "hours", and f(x) is a flow rate in "gallons per hour." 25. x is a position in "feet", and f(x) is an area in "square feet." 26. x is a position in "inches", and f(x) is a density in "pounds per inch." In problems 27 -31, represent the area with a definite integral and use technology to find the approximate answer. 27. The region bounded by y = x , the x-axis, the line x = 1, and x = 5. 177 28. The region bounded by y = Vx , the x-axis, and the line x = 9. 29. The shaded region shown to the right. y = Vx 30. The shaded region below. 31. Consider the definite integral | (3 + x) dx . 178 (a) Using six rectangles, find the left-hand Riemann sum for this definite integral. b) Using six rectangles, find the right-hand Riemann sum for this definite integral. c) Using geometry, find the exact value of this definite integral. 32. Consider the definite integral x' dx. (a) Using four rectangles, find the left-hand Riemann sum for this definite integral. (b) Using four rectangles, find the right-hand Riemann sum for this definite integral. 33. Write the total distance traveled by the car in the graph between 1 pm and 4 pm as a definite integral and estimate the value of the integral. velocity (miles/hour) 20 179textbroker.com X Final Exam X X Canvas LMS X MATH140-12141 (ONL) X BusCalc.pdf X *Dashboard X -> C A Not Secure | opentextbookstore.com/buscalc/BusCalc.pdf Update : Suggested Sites M Gmail YouTube Disney+ canvas find cards saved o... Other Bookmarks BusCalc.pdf 180 / 272 69% + 176 c) Using geometry, find the exact value of this definite integral. 32. Consider the definite integral | x' dx. (a) Using four rectangles, find the left-hand Riemann sum for this definite integral. (b) Using four rectangles, find the right-hand Riemann sum for this definite integral 33. Write the total distance traveled by the car in the graph between 1 pm and 4 pm as a definite integral and estimate the value of the integral. velocity (miles/hour) 177 Chapter 3 The Integral Business Calculus 180 areas Problems 34-41 refer to the graph of f shown. Use the y= f(x) graph to determine the values of the definite integrals. The bold numbers represent the area of each region.) 2 178 34. J f(x) dx 35. J f(x) dx 36. J f(x) dx 0 3 2 7 5 37. J f(w) dw 38. J f(x) dx 39. J f(x) dx 40. [ f(t) at 41 . J f ( x ) dx 6 3 Problems 42-47 refer to the graph of g shown. Use the graph to evaluate the integrals y = g(x) 42. J g(x) dx 43. J g(t) dt 44. J g(x) dx 179 45. J g(s) ds 46. f 2g(1) at 47. S 1+g(x) dx 5 AVA 180textbroker.com X Final Exam X X Canvas LMS X MATH140-12141 (ONL) X BusCalc.pdf X *Dashboard X -> C A Not Secure | opentextbookstore.com/buscalc/BusCalc.pdf Update : Suggested Sites M Gmail YouTube Disney+ canvas find cards saved o... Other Bookmarks E BusCalc.pdf 187 / 272 69% + Chapter 3 The Integral Business Calculus 187 3.2 Exercises In problems 1 - 5, verify that F(x) is an antiderivative of the integrand f(x) and use Part 2 of the Fundamental Theorem to evaluate the definite integrals. 1 . f 2 x dx , F ( x ) = 1 2 + 5 2 . f 3 x dx , F ( x ) = x 3 + 2 3 . fx ax , F( 1 ) = 3 x3 187 4 . S ( 12 + 4x - 3 ) dx , F ( x ) - 3 x3 + 212 - 3x 5 . fax , F( x ) = In( x ) 0 6. Given A(x) = S 2t dt, find A'(x) 0 7. Given A(x) = S (3-12) dt, find A'(x) y = f(t) 188 8. Let A(x) = J f(f) at for the function graphed here. Evaluate A'(1), A'(2) , A' ( 3 ) . KA For problems 9-10, the graph provided shows g'(x). Use it sketch a graph of g(x) that satisfies g(0) = 0. 189 9. 10. 190textbroker.com X Final Exam X X Canvas LMS X MATH140-12141 (ONL) X BusCalc.pdf X *Dashboard X -> C A Not Secure | opentextbookstore.com/buscalc/BusCalc.pdf Update : Suggested Sites M Gmail YouTube Disney+ canvas find cards saved o... Other Bookmarks E BusCalc.pdf 194 / 272 69% + Chapter 3 The Integral Business Calculus 194 3.3 Exercises For problems 1-10, find the indicated antiderivative 1. f(x3 -14x + 5)dx 2. [ (2.5x5 - x-1.25) dx 3. 12.3dy 4. [n'dw 193 5. fedp 6. [ Vitex - 1 dx 7. d 8. J dx 9. [ (x - 2)x + 2)dx 10. [ - at For problems 11-18, find an antiderivative of the integrand and use the Fundamental Theorem to evaluate the definite integral 5 11. J 3x2 dx 12. J x2 dx 13. S ( x2 + 4x - 3) dx 14. x dx 2 194 15 . [ xdx 16 . [ Vx dx 17 . 1 4 dx 18 . 1 1 dx - For problems 19 - 21 find the area shown in the figure. y= 4 3 + y = 1 +* y = (x- 2)2 y =x2 19 . 20. 21. 195 196