1    Compute the integral

$$\int_{0}^{8}\int_{\root 4\circ x}^2 {1\over y^4 +1} {\mathrm dy}{\mathrm dx}$$

2    Integrate the function $f(x,y,z) = x + y$ over the region bounded by the cylinder $x^2 + 3z^2 = 9$ and the planes $y=0$ and $x+y=3$.

3    Let $W$ be the region bounded by the coordinate planes and the surfaces $y=1-x$ and $y= \cos( {\pi\over 2} x)$, with $0\leq x\leq 1$. Find the volume of $W$.

4 Chapter 6.1 $\char93 4$

5    Evaluate the integral

$$\int_0^2\int_{x\over 2}^{{x\over 2} + 1} x^5 (2y-x) e^{(2y-x)^2} {\mathrm dy}{\mathrm dx}$$

by making the substitution $u = x$, $v= 2y-x$.

6    Chapter 6.3 $\char93 11$

7    Chapter 7.1 $\char93 14$ and Chapter 7.2 $\char93 6, 9, 15$

8    Chapter 4.4 $\char93 9, 24, 26$