1 / 16

Integral Calculus: U-Substitution & Change of Variables

Learn how to integrate using u-substitution and change of variables with step-by-step examples and guidelines. Understand pattern recognition in nested derivatives and check your solutions by taking derivatives. Explore even and odd functions in integral calculus.

jnutt
Download Presentation

Integral Calculus: U-Substitution & Change of Variables

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 by u-Substitution "Millions saw the apple fall, but Newton asked why." -– Bernard Baruch

  2. Objective • To integrate by using u-substitution

  3. Recognizing nested derivatives…

  4. What about…

  5. In summary… • Pattern recognition: • Look for inside and outside functions in integral • Determine what u and du would be • Take integral • Check by taking the derivative!

  6. Change of Variables

  7. Another example

  8. A third example

  9. Guidelines for making a change of variables • 1. Choose a u = g(x) • 2. Compute du • 3. Rewrite the integral in terms of u • 4. Evaluate the integral in terms of u • 5. Replace u by g(x) • 6. Check your answer by differentiating

  10. Try…

  11. Change of variables for definite integrals • Thm: If the function u = g(x) has a continuous derivative on the closed interval [a,b] and f is continuous on the range of g, then

  12. First way…

  13. Second way…

  14. Another example (way 1)

  15. Way 2…

  16. Even and Odd functions • Let f be integrable on the closed interval [-a,a] • If f is an even function, then • If f is an odd function then

More Related