Substitution and Symmetry

Homework reminder.
Quiz reminder: Friday, Jan 20 (Ace the first quiz!).
Office Hours: Tue 11-1.
Monday is a holiday!
Wednesday - areas between curves and volumes
First midterm: Wed Feb 1 at 7pm (review lecture during day!)
Quick 5 minute discussion of computers and Maxima.
Quiz format: one question on front; one on back.


  1. The total distance traveled is $ \int_{t_1}^{t_2} \vert v(t)\vert dt$ since $ \vert v(t)\vert$ is the rate of change of $ F(t)=$ distance traveled (your speedometer displays the rate of change of your odometer).
  2. How to compute $ \int_{a}^{b} \vert f(x)\vert dx$.
    1. Find the zeros of $ f(x)$ on $ [a,b]$, and use these to break the interval up into subintervals on which $ f(x)$ is always $ \geq 0$ or always $ \leq 0$.
    2. On the intervals where $ f(x) \geq 0$, compute the integral of $ f$, and on the intervals where $ f(x)\leq 0$, compute the integral of $ -f$.
    3. The sum of the above integrals on intervals is $ \int \vert f(x)\vert dx$.

This section is primarly about a powerful technique for computing definite and indefinite integrals.

William Stein 2006-03-15