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naomicervero
06.05.2020 •
Mathematics
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
Solved
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Ответ:
1. C. cylindrical coordinates
2 A. spherical coordinates
3. A. spherical coordinates
4. D. Cartesian coordinates
5 B. polar coordinates
Step-by-step 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
Ответ:
0.18 times j equals the value