1 / 30

Integration

Integration. This is not your father’s area?. Ask me what I should already know The pre-requisite questions. The exact mean value of the function f(x) from a to b is. y. 5. a. b. 2. c. x. 7. Given the f(x) vs x curve, and the magnitude of the areas as shown, the value of. -7

saral
Download Presentation

Integration

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Integration This is not your father’s area? http://nm.mathforcollege.com

  2. Ask me what I should already knowThe pre-requisite questions http://nm.mathforcollege.com

  3. The exact mean value of the function f(x) from a to b is http://nm.mathforcollege.com

  4. y 5 a b 2 c x 7 Given the f(x) vs x curve, and the magnitude of the areas as shown, the value of • -7 • -2 • 12 • Cannot be determined http://nm.mathforcollege.com

  5. y 5 a b 2 c x 7 Given the f(x) vs x curve, and the magnitude of the areas as shown, the value of • -7 • -2 • 7 • 12 http://nm.mathforcollege.com

  6. Physical examples http://nm.mathforcollege.com

  7. Distance Covered By Rocket http://nm.mathforcollege.com

  8. Concentration of Benzene u= velocity of ground water flow in the x -direction (m/s) D = dispersion coefficient (m2) C0= initial concentration (kg/m3) http://nm.mathforcollege.com

  9. Is Wal*** “short shifting” you? http://nm.mathforcollege.com

  10. Calculating diameter contraction for trunnion-hub problem http://nm.mathforcollege.com

  11. END http://nm.mathforcollege.com

  12. 7.02Trapezoidal Rule http://nm.mathforcollege.com

  13. Two-segment trapezoidal rule of integration is exact for integration of polynomials of order of at most • 1 • 2 • 3 • 4 http://nm.mathforcollege.com

  14. In trapezoidal rule, the number of segments needed to get the exact value for a general definite integral • 1 • 2 • 1 googol • infinite http://nm.mathforcollege.com

  15. In trapezoidal rule, the number of points at which function is evaluated for 8 segments is • 8 • 9 • 16 • 17 http://nm.mathforcollege.com

  16. In trapezoidal rule, the number of function evaluations for 8 segments is • 8 • 9 • 16 • 17 http://nm.mathforcollege.com

  17. The distance covered by a rocket from t=8 to t=34 seconds is calculated using multiple segment trapezoidal rule by integrating a velocity function. Below is given the estimated distance for different number of segments, n. • 1 • 2 • 3 • 4 The number of significant digits at least correct in the answer for n=5 is http://nm.mathforcollege.com

  18. The velocity vs time is given below. A good estimate of the distance in meters covered by the body between t=0.5 and 1.2 seconds is • 213*0.7 • 256*0.7 • 256*1.2-213*0.5 • ½*(213+256)*0.7 http://nm.mathforcollege.com

  19. 7.05Gauss Quadrature Rule http://nm.mathforcollege.com

  20. The morning after learning Gauss Quadrature Rule… http://nm.mathforcollege.com

  21. is exactly http://nm.mathforcollege.com

  22. A scientist would derive one-point Gauss Quadrature Rule based on getting exact results of integration for function f(x)=a0+a1x. The one-point rule approximation for the integral is http://nm.mathforcollege.com

  23. For integrating any first order polynomial, the one-point Gauss quadrature rule will give the same results as • 1-segment trapezoidal rule • 2-segment trapezoidal rule • 3-segment trapezoidal rule • All of the above http://nm.mathforcollege.com

  24. A scientist can derive a one-point quadrature rule for integrating definite integrals based on getting exact results of integration for the following function • a0+a1x+a2x2 • a1x+a2x2 • a1x • a2x2 http://nm.mathforcollege.com

  25. For integrating any third order polynomial, the two-point Gauss quadrature rule will give the same results as • 1-segment trapezoidal rule • 2-segment trapezoidal rule • 3-segment trapezoidal rule • None of the above http://nm.mathforcollege.com

  26. The highest order of polynomial for which the n-point Gauss-quadrature rule would give an exact integral is • n • n+1 • 2n-1 • 2n http://nm.mathforcollege.com

  27. END http://nm.mathforcollege.com

  28. Physically, integrating means finding the • Area under the curve from a to b • Area to the left of point a • Area to the right of point b • Area above the curve from a to b http://nm.mathforcollege.com

  29. The velocity of a body is given as v(t)=t2. Given that • 27 • 54 • 63 • Cannot be determined the location of the body at t=6 is http://nm.mathforcollege.com

  30. The velocity of a body is given as v(t)=t2. Given that • 27 • 54 • 63 • Cannot be determined the distance covered by the body between t=3 and t=6 is http://nm.mathforcollege.com

More Related