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Math Quiz 3 Review: Integration Techniques and Curveballs

This math quiz review covers various integration techniques, including algebraic simplification, trigonometric and non-trigonometric substitution, parts rule, and partial fractions. It also includes challenging curveball questions and tricky treats related to areas under curves, average completion time, and median scores.

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Math Quiz 3 Review: Integration Techniques and Curveballs

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  1. October 18, 2007 Welcome back! … to the cavernous pit of math

  2. Quiz 3 Review

  3. JEOPARDY

  4. FINAL JEOPARDY

  5. Give one example for each technique or description. You have five minutes! • Algebraic simplification of the integrand • Rewriting the integrand using trig identities, then substitution • Substitution (non-trig) • Trig substitution • Parts once • Parts seven times • Substitution, then parts • Partial fractions • Type I improper integral that converges • Type II improper integral • May not be integrated using any technique

  6. Integration Nation (100) Do the first step:

  7. Integration Nation (200) Do the first step:

  8. DAILY DOUBLE

  9. Integration Nation (300) Do the first step:

  10. Integration Nation (400) Do the first step:

  11. Integration Nation (500) Do the first step:

  12. Curveballs (100) Find the area under the curve for 1 ≤ x <  or show that it is infinite.

  13. Curveballs (200) Suppose x is the number of hours it takes a random student to complete an exam and the curve is the density function for x. Find the average completion time.

  14. Curveballs (300) Find the area under the curve Hint: there is an easy way to do this problem and a hard way to do it. Do it the easy way!

  15. Curveballs (400) Draw a picture that explains why the statement is true: Determine whether each integral converges or diverges.

  16. Curveballs (500) Find the area under from x = 0 to x = .

  17. Tricky Treats (100) Evaluate

  18. Tricky Treats (200) Suppose x is the score of a student on a test, and the density function for x is symmetric around the line x = 75. What is the median student score on the test?

  19. Tricky Treats (300) Evaluate

  20. Tricky Treats (400) Find a function f(x) so that BUT diverges.

  21. DAILY DOUBLE

  22. Tricky Treats (500) Rewrite the integral as the sum of limits of proper integrals:

  23. Potpourri (100) Break into partial fractions:

  24. Potpourri (200)

  25. Potpourri (300)

  26. Potpourri (400) Evaluate or show that it diverges:

  27. Potpourri (500) Suppose the density function for the time spent waiting for a call to be answered is where x is the waiting time in minutes and A is a constant. Find the value of A.

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