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.

Remarks:

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.