Review for Second Exam

1. Page 333, problems 5, 6, 7, 9, 12, 13, 15, 16, 26 and 38.
2. Page 351, problems 7, 8 and 15.
3. Find the area of the region enclosed by $y=x$ and $y=\sqrt[3]{x}$ .
4. Find the area of the region enclosed by $y=12-x^{2}$ and $y=x^{2}-6$ .
5. Find the area of the region enclosed by $y=\sqrt{x+3}$ and $y=(x+3)/2$ .
6. Find the area of the region enclosed by $y=1+\sqrt{x}$ and $y=(3+x)/3$ .
7. Page 358, problems 4, 6, 11, 21 and 22.
8. Find the arc length of $${y=\frac{x^{3}}{6} + \frac{1}{2x}}$$ for $\frac{1}{2} \le x \le 1$ .
9. What is the arc length of the curve $y = 20 \cosh (x/20) -15$ for $-7 \le x \le 7$ ?
   Hint: $(\cosh u)^{\prime}=\sinh u$ , $(\sinh u)^{\prime}=\cosh u$ , $\cosh^{2} u - \sinh^{2} u = 1$ .
10. Find the volume of the solid obtained by rotating the region bounded by $y=x$ and $y=\sqrt{x}$ about $y=1$ .
11. Find the volume of the solid obtained by rotating the region bounded by $y=x^{4}$ and $y=1$ about $y=2$ .
12. Find the volume of a solid formed by rotating the curve $y=1/x$ for $1 \le x < \infty$ around the $x$ axis.
13. Page 366, problem 3.
14. Page 375, problem 3.