15.6. Parametric Surfaces and Their Areas
Ex. 1
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Ex. 2
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Ex. 4
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Ex. 5
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Ex. 7
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Ex. 8
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Ex. 9
Tangent Plane: -2*x - 4*y + 4*z - 6 == 0 Tangent Plane: -2*x - 4*y + 4*z - 6 == 0 Sleeping...
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Ex. 10
16*pi 16*pi |
Ex. 11
-1/6*pi + 1/6*(37*sqrt(37))*pi -1/6*pi + 1/6*(37*sqrt(37))*pi |
15.7. Surface Integrals
Ex. 1
sin(p)^2 sin(p)^2 |
4/3*pi 4/3*pi |
Ex. 2
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13/3*sqrt(2) 13/3*sqrt(2) |
Ex. 3
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1 1 |
3/2*pi 3/2*pi |
sqrt(2)*pi sqrt(2)*pi |
Ex. 4
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4/3*pi 4/3*pi |
Ex. 5
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1/2*pi 1/2*pi |
0 0 |
15.8. Stokes’ Theorem
Ex. 1
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(0, 0, 2*y + 1) (0, 0, 2*y + 1) |
pi pi |
Ex. 2
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[[x == r1, y == -sqrt(-r1^2 + 1), z == -sqrt(3)], [x == r2, y == -sqrt(-r2^2 + 1), z == sqrt(3)], [x == r3, y == sqrt(-r3^2 + 1), z == -sqrt(3)], [x == r4, y == sqrt(-r4^2 + 1), z == sqrt(3)]] [[x == r1, y == -sqrt(-r1^2 + 1), z == -sqrt(3)], [x == r2, y == -sqrt(-r2^2 + 1), z == sqrt(3)], [x == r3, y == sqrt(-r3^2 + 1), z == -sqrt(3)], [x == r4, y == sqrt(-r4^2 + 1), z == sqrt(3)]] |
0 0 |
15.9. The Divergence Theorem
Ex. 1
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1 1 |
Ex. 2
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3*y 3*y |
184/35 184/35 |
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