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

Quiz 3 Review

JEOPARDY Integration Nation CurveballsTricky TreatsPotpourri

FINAL JEOPARDY

Give one example for each technique or description. You have five minutes! 1.Algebraic simplification of the integrand 2.Rewriting the integrand using trig identities, then substitution 3.Substitution (non-trig) 4.Trig substitution 5.Parts once 6.Parts seven times 7.Substitution, then parts 8.Partial fractions 9.Type I improper integral that converges 10.Type II improper integral 11.May not be integrated using any technique

Integration Nation (100) Do the first step:

Integration Nation (200) Do the first step:

DAILY DOUBLE

Integration Nation (300) Do the first step:

Integration Nation (400) Do the first step:

Integration Nation (500) Do the first step:

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

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.

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!

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

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

Tricky Treats (100) Evaluate

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?

Tricky Treats (300) Evaluate

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

DAILY DOUBLE

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

Potpourri (100) Break into partial fractions:

Potpourri (200)

Potpourri (300)

Potpourri (400) Evaluate or show that it diverges:

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.