Review for the Final

1. All the problems in Exams 1-4.
2. For two curves $\sin x$ and $\cos x$ , find the shaded area shown in the figure.
   
3. What is the arc length of the curve $y = 20 \cosh (x/20) -15$ for $-7 \le x \le 7$ ?
   
4. Exercises 1-15, page 429.
5. Express the repeating decimal $1.2345345345345 \ldots$ as a fraction.
   Hint: use the fact that $1.2345345345=1.2 + 0.0345 + 0.0000345 + 0.0000000345 + \ldots$ to write $1.2345345345 \ldots$ as a geometric series.
6. Estimate the value of $\int_{0}^{1} (\sin x/x) dx$ by approximating the function $\sin x/x$ with a Taylor polynomial of degree $4$ .
7. Estimate the value of $\int_{0}^{1} e^{-x^{2}} dx$ by approximating the function $e^{-x^{2}}$ with a Taylor polynomial of degree $6$ .
8. After 3 days a sample of radon ($^{222}$ Rn) decayed to 58% of its original amount. How long will it take the sample to decay to 10% of its original amount?