∫∫∑ 1 / √ (1 + 4x & # 178; + 4Y & # 178;) ds, ∑ surface z = x & # 178; + Y & # 178; (0 ≤ Z ≤ 1)
z=x²+y²
z'x=2x z'y=2y
ds=√(1+4x²+4y²)dxdy
∫∫Σ1/√(1+4x²+4y²)ds
=∫∫dxdy
=π
RELATED INFORMATIONS
- 1. 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
- 2. 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,
- 3. What does DS represent in the surface integral of area in higher numbers
- 4. 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
- 5. Let ∑ be the cylinder x ^ 2 + y ^ 2 = a ^ 2 at 0
- 6. 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
- 7. The focal point F of the parabola is on the positive half axis a (M. - 3) of the x-axis, and the standard equation is solved on the parabola AF5
- 8. The distance from the focus to the collimator is 5, and the parabolic standard equation is solved RT.
- 9. The standard equation of parabola with focus f (0, - 4) is?
- 10. If we know that the focal coordinate of parabola is f (0, - 2), then its standard equation is?
- 11. ∫ (X & ∫ 178; + Y & ∫ 178;) ds ∑: z = root X & ∫ + Y & ∫ 178; the part cut off by z = 2 ∫ ∫ is followed by ∑
- 12. 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
- 13. ∫∫ 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
- 14. 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)
- 15. Find ∫ DS, where l is the circle x2 + y2 = 4
- 16. High number LIM (x - > 0) TaNx / x ^ 3-x ^ 2-2x why TaNx ~ x ^ 3-x ^ 2-2x ~ (- 2x)
- 17. High number: l is the circle x square + y square; find L (x square + y Square) ds under ∮
- 18. 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?
- 19. 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=
- 20. 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