14.3. Double Integrals in Polar Coordinates
Ex. 1
15/2*pi 15/2*pi |
Ex. 2
1/2*pi 1/2*pi |
Ex. 3
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1/8*pi 1/8*pi |
Ex. 4
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3/2*pi 3/2*pi |
Exercise 1
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2*pi 2*pi |
14.5. Surface Area
Ex. 1
-5/12*sqrt(5) + 9/4 -5/12*sqrt(5) + 9/4 |
Ex. 2
-1/6*pi + 1/6*(37*sqrt(37))*pi -1/6*pi + 1/6*(37*sqrt(37))*pi |
Exercise 1
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[[x == r1, y == -sqrt(-r1^2 + 3), z == 3], [x == r2, y == sqrt(-r2^2 + 3), z == 3], [x == r3, y == -I*r3, z == 0], [x == r4, y == I*r4, z == 0]] [[x == r1, y == -sqrt(-r1^2 + 3), z == 3], [x == r2, y == sqrt(-r2^2 + 3), z == 3], [x == r3, y == -I*r3, z == 0], [x == r4, y == I*r4, z == 0]] |
[z == -sqrt(-x^2 - y^2 + 4) + 2, z == sqrt(-x^2 - y^2 + 4) + 2] [z == -sqrt(-x^2 - y^2 + 4) + 2, z == sqrt(-x^2 - y^2 + 4) + 2] |
4*pi 4*pi |
14.6. Triple Integrals
Ex. 1
27/4 27/4 |
Ex. 2
1/24 1/24 |
Ex. 3
128/15*pi 128/15*pi |
Ex. 5
1/3 1/3 |
Exercise 1
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[x == -1, x == 1] [x == -1, x == 1] |
-16/3 -16/3 |
Exercise 2
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20*pi 20*pi |
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