Review for the Final

1. All the problems in Exams 1-4.
2. Reviews for Exams 1-4.
3. Find the global and local maxima and minima of the following functions.

   1. $$F(x) = \int_{0}^{x} \frac{\sin t}{t} \, dt ,$$   for$$\ \pi/4 \le x \le 9 \pi/4.$$

   2. $$F(x) = \int_{0}^{x} \sin \left( \frac{\pi t^{2}}{2} \right) \, dt ,$$   for$$\ -\pi/4 \le x \le \pi/2.$$

4. The curve in the figure is defined by $y=3 x^{2} - 3$ ; find the exact area of the shaded region.
   
5. The curves in the figure are defined by $y=\vert x\vert$ and $y=x^{2}-2$ ; find the exact area of the shaded region.