we have PROBLEMS 14.7 Section 14.7 The Fundamental Theorem of integral Caloukus 999 2. (9) he rate of 5x dx 43. where f(r)- 3. 4. uffices to -5x dx (2r - 3) dx 44. Evaluate 6. xpx 5. o² + 7. + 4y + 4) dy 45. Suppose f(x)D -1 dr. Evaluate 3 dt. 8. &p (66-) (2t-3r2) dt 46. Evaluate | 9. 10. + xp xp 47. If 3/2 12. f(x) dx 5 and 3. x2 3/2 11. %3D Vx4 dx 8. 13. 14. 48. If f) dx =5, and *9 = xp (x) fx) dx = 2, find xp 1 1/2 16. xp (+x+) cost xp xp (x)f 15. 49. Evaluate (z + 1)* dz xp (- x^)| 181 18. xp (Hint: It is not necessary to find 2 17. xp xp ence -2 2x²(x³ – 1) dx xp (/1-X - €/) 19. 20. (x+ 2)³ dx e -e 1= (x)f In discussing traffic safety, Shonles 50. Suppose that f(x) = (300 22. dt where x > e. Find f'(x). %3D et +e-t 4. Ap – 51. Severity Index considers how much acceleration a person can tolerate in a crash so that there is no major injury. The severity index is defined as 21. 2. xp Bronb xp Lonoiens 23. 24. CT X - 1 xp 5/2 12 dt = T'S 26. | (3x2 + 4x)(x + 2x?)* dx where a (a Greek letter read "alpha") is considered a constant involved with a weighted average acceleration, and T is the duration of the crash. Find the severity index. 25. xp bioqne 3. (x+3)2 20/3 28. nou-1/3 27. xp V3x + 5 dx /10- 3p dp av9? +3 dg bp 30. 29. 1/3 31. 32. dx (x² + 1)2/3 - xP I + pXLA* / 9. 33. 34. (m + ny) dy 52. Statistics In statistics, the mean u (a Greek letter reac xp “mu") of the continuous probability density function f defin the interval [a, b] is given by - 35. 36. 8|x| dx xp -2 xp (x) fx 37. | 3(x-2 +x-3 –x-4) dx and the variance o? (o is a Greek letter read "sigma") is g xp 39. (x+1)e+2* dx 1. | 38. = ,0 xp (X) f-(ri – x) = Compute u and then o? if a = 0, b = 1, and f (x) = 6(x The economist Pareto a. %3D %3D 95 xp In e 40. 53. Distribution of Incomes 2++6x* +x³ + 8x2 +x+ 5 x3 + 5x + 1 an empirical law of distribution of higher incomes that number N of persons receiving x or more dollars. If 41. xp NP =-Ar-B xp 42. dx (Hint: Multiply the integrand by ) J. I. Shonle, Environmental Applications of General Physics C Addison-Wesley Publishing Company, Ic., 1975). G. Tintner, Methodology of Mathematical Economics and Ec (Chicago: University of Chicago Press, 1967), p. 16.
we have PROBLEMS 14.7 Section 14.7 The Fundamental Theorem of integral Caloukus 999 2. (9) he rate of 5x dx 43. where f(r)- 3. 4. uffices to -5x dx (2r - 3) dx 44. Evaluate 6. xpx 5. o² + 7. + 4y + 4) dy 45. Suppose f(x)D -1 dr. Evaluate 3 dt. 8. &p (66-) (2t-3r2) dt 46. Evaluate | 9. 10. + xp xp 47. If 3/2 12. f(x) dx 5 and 3. x2 3/2 11. %3D Vx4 dx 8. 13. 14. 48. If f) dx =5, and *9 = xp (x) fx) dx = 2, find xp 1 1/2 16. xp (+x+) cost xp xp (x)f 15. 49. Evaluate (z + 1)* dz xp (- x^)| 181 18. xp (Hint: It is not necessary to find 2 17. xp xp ence -2 2x²(x³ – 1) dx xp (/1-X - €/) 19. 20. (x+ 2)³ dx e -e 1= (x)f In discussing traffic safety, Shonles 50. Suppose that f(x) = (300 22. dt where x > e. Find f'(x). %3D et +e-t 4. Ap – 51. Severity Index considers how much acceleration a person can tolerate in a crash so that there is no major injury. The severity index is defined as 21. 2. xp Bronb xp Lonoiens 23. 24. CT X - 1 xp 5/2 12 dt = T'S 26. | (3x2 + 4x)(x + 2x?)* dx where a (a Greek letter read "alpha") is considered a constant involved with a weighted average acceleration, and T is the duration of the crash. Find the severity index. 25. xp bioqne 3. (x+3)2 20/3 28. nou-1/3 27. xp V3x + 5 dx /10- 3p dp av9? +3 dg bp 30. 29. 1/3 31. 32. dx (x² + 1)2/3 - xP I + pXLA* / 9. 33. 34. (m + ny) dy 52. Statistics In statistics, the mean u (a Greek letter reac xp “mu") of the continuous probability density function f defin the interval [a, b] is given by - 35. 36. 8|x| dx xp -2 xp (x) fx 37. | 3(x-2 +x-3 –x-4) dx and the variance o? (o is a Greek letter read "sigma") is g xp 39. (x+1)e+2* dx 1. | 38. = ,0 xp (X) f-(ri – x) = Compute u and then o? if a = 0, b = 1, and f (x) = 6(x The economist Pareto a. %3D %3D 95 xp In e 40. 53. Distribution of Incomes 2++6x* +x³ + 8x2 +x+ 5 x3 + 5x + 1 an empirical law of distribution of higher incomes that number N of persons receiving x or more dollars. If 41. xp NP =-Ar-B xp 42. dx (Hint: Multiply the integrand by ) J. I. Shonle, Environmental Applications of General Physics C Addison-Wesley Publishing Company, Ic., 1975). G. Tintner, Methodology of Mathematical Economics and Ec (Chicago: University of Chicago Press, 1967), p. 16.
Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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