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∫ (x ^ 2-y ^ 2) dydz + (y ^ 2-z ^ 2) dzdx + (Z ^ 2-x ^ 2) DXDY how to use Gauss formula? S is the upper half ellipsoid x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 + Z ^ 2 = 1 (z > = 0), take the upper side, and the Gauss formula is ∫ ∫ (x + y + Z) DV, which will not be done later
The integral region is symmetric with respect to both the xoz plane and the YOZ plane, so the integral of the two odd functions X and Y is 0. The original integral = ∫∫∫ Z DV is calculated by the cross section method = ∫ [0 → 1] Z DZ ∫∫ 1 DXDY. The integral region of the double integral is the cross section: X & # 178 / / A & # 178; + Y & # 178 / / B & # 178; ≤ 1-z & ∫ 178; the integrand is 1, the product
RELATED INFORMATIONS
- 1. The surface integral ∫ ∫ xdydz + y ^ 2dzdy + zdxdy, ∑ is the upper side of the triangle on the plane where x + y + Z = 1 is cut by the coordinate plane
- 2. Is it possible to cut a conic section with a plane
- 3. Use a plane to cut off a cylinder and a cone. The shape of the section is the same ()
- 4. The shape of the cross section of a plane passing through the apex of a cone may be
- 5. Use a plane to cut a cone and a sphere. What are the shapes of the cross sections?
- 6. As shown in the figure, the cross-section of a plane passing through the apex of a cone is () A. B. C. D.
- 7. If a cone is cut by a plane, can the cross section be a triangle? A right triangle? When the cross section is a circle
- 8. When the plane is cut perpendicular to the cone axis, the shape of the intersection line is (); when the plane is cut parallel to the cone axis, the shape of the intersection line is () When the plane cuts perpendicular to the cone axis, the shape of the intersection line is (); when the plane cuts parallel to the cone axis, the shape of the intersection line is (); when the plane cuts through the cone vertex, the shape of the intersection line is ()
- 9. The section plane intersects with the axis of the cone A. Circle B. Intersect two lines C. Ellipse
- 10. If the plane of the plane section is perpendicular to the axis of the cone, what is the intersection line?
- 11. The surface integral ∫ (y ^ 2-x) dydz + (Z ^ 2-y) dzdx + (x ^ 2-z) DXDY, ∑ is Z = 1-x ^ 2-y ^ 2, which is located on the upper side above the side
- 12. Surface integral ∫ ∫ xdydz + Z ^ 2dxdy / (x ^ 2 + y ^ 2 + Z ^ 2), where surface ∑ is surrounded by x ^ 2 + y ^ 2 = R ^ 2 and z = R, z = - R
- 13. Using Gauss formula, we can find the surface fraction ∮ XY ^ 2dydz + YZ ^ 2dzdx + ZX ^ 2dxdy, where ∑ is the outside of the sphere x ^ 2 + y ^ 2 + Z ^ 2 = R ^ 2 The reference answer is 4 π R ^ 5 / 5. But I'm always 2 π R ^ 5 / 5 My score is settled on the spot. My adoption rate is 100% Let P = XY & # 178;, q = YZ & # 178;, r = ZX & # 178; ∵αP/αx=y²,αQ/αy=z²,αR/αz=x² The original formula = ∫ ∫ (α P / α x + α Q / α y + α R / α z) dxdydz is obtained from Gauss formula =∫∫∫(x²+y²+z²)dxdydz =∫dθ∫sinφdφ∫r^4dr =(2π)[0--(1)](R^5/5-0) =2πR^5/5
- 14. Let the tangent plane of the point (x, y, z) on the surface ∑: x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 + Z ^ 2 / C ^ 2 = 1 be π, and calculate the surface integral ∫ ∫ ∑ 1 / λ DS, where λ is the distance from the coordinate origin to π
- 15. The domain of surface integral (x ^ 2 + y ^ 2) DS is bounded by z = x ^ 2 + y ^ 2 and z = 1 The answer is (5 radical 5 + 6) / 12 seeking process or seeking correct answer (the answer may be wrong)
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- 17. The shape of a window of a building is shown in the figure. The upper part is a semicircle, and the lower part is two windows with the same shape, m in length and N in width Rectangle, calculating (1) Total length of window and window frame (2) When m = 50cm, n = 20cm, what are the area of the window and the total length of the window frame
- 18. How should doors and windows be represented in the floor plan?
- 19. Is y = x ^ 2 + x a power function? Why?
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