Match the integrals with the type of coordinates which make them the easiest to do. Put the letter of the coordinate system to the left of the number of the integral.

 1. $\displaystyle \int \!\! \int \!\! \int_E \ dV$ where E is: $x^2+y^2+z^2 \leq 4, \ \ x \geq 0, \ \ y \geq 0, \ \ z \geq 0$
 2. $\displaystyle \int \!\! \int \!\! \int_E \ z \ dV$ where E is: $1 \leq x \leq 2, \ \ 3 \leq y \leq 4, \ \ 5 \leq z \leq 6$
 3. $\displaystyle \int_{0}^{1} \! \int^{y^2}_{0} \ \frac{1}{x} \ dx \ dy$
 4. $\displaystyle \int \!\! \int_D \ \frac{1}{x^2+y^2} \ dA$ where D is: $x^2+y^2 \leq 4$
 5. $\displaystyle \int \!\! \int \!\! \int_E \ z^2 \ dV$ where E is: $-2 \leq z \leq 2, \ \ 1 \leq x^2+y^2 \leq 2$

A. spherical coordinates
B. cartesian coordinates
C. polar coordinates
D. cylindrical coordinates