Review for 4th Exam

1. Exercises 1-21, page 284.
2. Exercises 30-35, page 285.
3. Exercises 3-18, page 296.
4. Problems 14-19, page 281.
5. Find the area enclosed by $y=x(x-\pi)$ and $y= \sin x$ .
6. Find the area enclosed by $y=\vert x\vert$ and $y=x^2-2$ .
7. Evaluate the integral $\int_{0}^{3} \vert 3 x^2 - 3\vert dx$ .
8. Find the exact average value of $f(x)=\sqrt{x}$ on the interval $0 \le x \le 9$ .
9. If $f$ is continuous and $\int_{0}^{4} f(x) \, d x = 10$ , find $\int_{0}^{2} f(2 x) \, d x$ .