![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
Calculate the surface integral ∫ (x ^ 2 + y ^ 2 + Z ^ 2) ^ - 0.5ds, where ∑ is the sphere x ^ 2 + y ^ 2 + Z ^ 2 = a ^ 2 (z > 0)
∫∫(x^2+y^2+z^2）^-0.5ds
=∫∫ads
=a*(2πa²)
=2πa³
Surface integral can simplify integrand function by surface equation; integrand function is 1, integral result is surface area; sphere surface area is 4 π A & # 178; because z > 0, this problem is only half sphere, so it is 2 π A & # 178;
RELATED INFORMATIONS
- 1. ∫∫ s (x + y + Z) ds, where s is the upper hemisphere, z = √ a ^ 2-x ^ 2-y ^ 2 Detailed point, this is a class of surface integral problem
- 2. Given the coordinates (1,2 times the root sign 3) of the endpoint B of the line segment AB, the endpoint a moves on the circle P (x + 1) ^ 2 + y ^ 2 = 4, find the tangent equation of the trajectory of the midpoint m in AB and P passing through point B
- 3. ∫ (X & ∫ 178; + Y & ∫ 178;) ds ∑: z = root X & ∫ + Y & ∫ 178; the part cut off by z = 2 ∫ ∫ is followed by ∑
- 4. ∫∫∑ 1 / √ (1 + 4x & # 178; + 4Y & # 178;) ds, ∑ surface z = x & # 178; + Y & # 178; (0 ≤ Z ≤ 1)
- 5. The equation for the projection of the sphere x ^ 2 + y ^ 2 + Z ^ 2 = 9 and the plane x + y = 1 on the xoy plane
- 6. The projection of the intersection line of x ^ 2 + y ^ 2 under the equation z = x ^ 2 + y ^ 2 and z = 2-radical on xoy plane,
- 7. What does DS represent in the surface integral of area in higher numbers
- 8. Let s be a sphere x ^ 2 + y ^ 2 + Z ^ 2 = 1, and find the value of surface integral ∫ (x + y + Z + 1) ds. The answer is 4 Π
- 9. Let ∑ be the cylinder x ^ 2 + y ^ 2 = a ^ 2 at 0
- 10. Let D: x ^ 2 + y ^ 2 + Z ^ 2 = a ^ 2, then what is the area of ∫ (x + y + Z) ^ 2ds curve divided into? (on D) The answer is 4 Π a ^ 4
- 11. Find ∫ DS, where l is the circle x2 + y2 = 4
- 12. High number LIM (x - > 0) TaNx / x ^ 3-x ^ 2-2x why TaNx ~ x ^ 3-x ^ 2-2x ~ (- 2x)
- 13. High number: l is the circle x square + y square; find L (x square + y Square) ds under ∮
- 14. If you translate the straight line y = - 2x + 6 downward by how many units, you can get that there is only one intersection point between the new straight line and the hyperbola y = 1 / x?
- 15. As shown in the figure, the straight line y = 2x moves 2 units along the positive direction of x-axis, intersects with X-axis at point a, and intersects with hyperbola y = 6 / X and hyperbola y = K / X at two points BC respectively, And the area of triangle OBC = the area of triangle OAB, K=
- 16. It is known that the absolute value of x = 4, the absolute value of y = 1 / 2, and XY is less than 0, the absolute value of X of y of the ball The writing process is the best
- 17. Let l be a line segment from a (1,0) to B (- 1,2), then the curve integral ∫ L (x + y) ds
- 18. Find the curve integral ∫ L (x + y) ds, l is the straight line segment connecting (1.0) (0.1) two points. (PS: explain how DS is transformed into DX)
- 19. I = FF (x ^ 2 + y ^ 2) ds, where the surface is spherical x ^ 2 + y ^ 2 + Z ^ 2 = 2 (x + y + Z)
- 20. Let ∑ be a sphere x ^ 2 + y ^ 2 + Z ^ 2 = 4, then the curved area is divided into ∮ (x ^ 2 + y ^ 2 + Z ^ 2) ds=