Question

Match the integrals with the type of coordinates which make them the easiest to do.

equation editorEquation Editor
1. ∭E dV where E is:
x^2 + y^2 + z^2<= 4, x>= 0, y>= 0, z>= 0
2. ∭E z^2 dV where E is:
-2 <= z <= 2,1 <= x^ 2 + y^2 <= 2
3. ∭E z dV where E is:
1 <= x <= 2, 3<= y <= 4,5 <= z <= 6
4. ∫10∫y^20 1/x dx
5. ∬D 1/x^2 + y^2 dA where D is: x^2 + y^2 <=4
Options:
A. spherical coordinates
B. polar coordinates
C. cylindrical coordinates
D. cartesian coordinates

Answer 1

1. C. cylindrical coordinates

2 A. spherical coordinates

3. A. spherical coordinates

4. D. Cartesian coordinates

5 B. polar coordinates

Explanation:

USE THE BOUNDARY INTERVALS TO IDENTIFY

1. ∭E dV where E is:

x^2 + y^2 + z^2<= 4, x>= 0, y>= 0, z>= 0 -- This is A CYLINDRICAL COORDINATES SINCE x>= 0, y>= 0, z>= 0

2. ∭E z^2 dV where E is:

-2 <= z <= 2,1 <= x^ 2 + y^2 <= 2 This is A SPHERICAL COORDINATES

3. ∭E z dV where E is:

1 <= x <= 2, 3<= y <= 4,5 <= z <= 6 -- This is A SPHERICAL COORDINATES

4. ∫10∫y^20 1/x dx ---- This is A CARTESIAN COORDINATES

5. ∬D 1/x^2 + y^2 dA where D is: x^2 + y^2 <=4 This is A POLAR COORDINATES