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Using spherical coordinates to calculate triple integral I = ∫∫∫ Z ^ 2dV, where the graph is composed of x ^ 2 + y ^ 2 + Z ^ 2
Calculate the triple integral fffz ^ 2dxdydz, where is the space area bounded by the ellipsoid x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 + Z ^ 2 / C ^ 2 = 1,
What I want to know is how to integrate X and y
It can be solved by section method
The spatial region can be expressed as {(x, y, z) | x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2
Can you help me understand the cubic integral? If the quadratic integral is volume, then the cubic integral is four-dimensional. I can't understand it. Which one do you choose
Mathematical dimension, generally speaking, is related to the number of variables,
The first integration space is a two-dimensional plane, the number of variables is 1, the variables can be changed on the horizontal axis of the coordinate axis, and the function value represents the ordinate, so the ordinate value can be obtained according to the change of the abscissa of the function. The second integration space is a three-dimensional solid, and there are two variables, which can be changed on the horizontal and vertical axis of the coordinate axis respectively, and the vertical coordinate Z value can be obtained according to the change of X and y, This is exactly the geometry in three dimensions. The cubic integral space is four-dimensional and has three variables. After that, we can't directly observe its geometry. Its variables are x, y, Z. and its function value represents an attribute, such as mass, pressure, etc. to find the mass of a three-dimensional object is to find the cubic integral of the density function of the geometry
It includes the use of percentage and ratio
About 35 questions each
For example, 1.3 billion, a relatively large number of applications
1. A dictionary is priced at 18 yuan and sold at a 20% discount, which is still 20% higher than the cost price. What is the cost price of this dictionary? 20% discount = 80% 18 × 80% = 14.4 yuan 14.4 ^ (1 + 20%) = 12 yuan. 2. The washing machine factory produced 7200 washing machines in the first quarter, 20% more than planned. How many washing machines are planned to be produced in the first quarter
Sixth grade mathematics calculation + application problem
Calculation questions:
(1) 6 / 2-13 / 26 / 9-2 / 3
(2) (0.75-3 / 16) × (2 / 9 + 1 / 3)
(3) [1 - (1 / 4 + 3 / 8)] 1 / 4
How high is the floor of Xiaoping's house? Xiaoping said: this building has 15 floors, and my family lives on the sixth floor
2. Uncle Li said: This paper is too long. It took 3 hours to input 1 / 3 of the total
At this rate, Uncle Li works for 8 hours, how many parts of this paper can he input? How many parts are left unfinished?
3. There are 240kg fruit candy in total, 1kg per 4 bags. Only 3 / 4 of them have been filled. How many bags have they filled?
2-6 / 13 △ 9 / 26-2 / 3 = 2-2 / 3-2 / 3 = 2 / 3 (0.75-3 / 16) x (2 / 9 + 1 / 3) = (3 / 4-3 / 16) x (2 / 9 + 3 / 9) = 9 / 16x5 / 9 = 5 / 16 [1 - (1 / 4 + 3 / 8)] / / 1 / 4 = (1-5 / 8) / / 1 / 4 = 3 / 242x (6-1) / 15 = 14, because the floor can only calculate the height of the fifth floor for 3 hours, then 1 / 3 △ 3 =
Volume problems in grade six
Six cuboids, 3cm long, 2cm wide and 1cm high, are used to make a big cuboid
There are different spelling methods, in which the largest surface area is, and the smallest surface area is. The volume of the large rectangle is compared with the sum of the original six cuboids
There are three different spelling methods, the largest surface area is 22, and the smallest surface area is 14. Compared with the volume sum of the original six cuboids, the volume of the large cuboid is the same as that of the small cuboid
Application of cuboid volume in Grade 6
1. A wood with a square cross section is 6.8 meters long. After sawing it into three cuboids, the surface area increases by 16 square meters?
2. A rectangular iron box with a square bottom. If you unfold its side, you will get a square with a side length of 8 decimeters. Calculate the volume of the iron box
1. A wood with a square cross section is 6.8 meters long. After sawing it into three cuboids, the surface area increases by 16 square meters
Practical problems of cylinder volume in Grade 6
1. A rectangular lead block with a length of 9cm, a width of 7cm and a height of 3cm and a cube lead block with an edge length of 5cm are cast into a cylinder. The diameter of the bottom surface of the cylinder is 20cm. What is the height of the cylinder?
2. A cuboid tank is 4 decimeters long, 3 decimeters wide and 2 decimeters high. It is full of diesel oil. Now pour the diesel oil into a cylinder with a diameter of 4 decimeters on the bottom. There is 3 / 5 space in the cylinder. Calculate the height of the cylinder
1. The height is: (9 × 7 × 3 + 5 × 5 × 5) △ 1 (CM)
2. Height of cylindrical oil drum: (4 × 3 × 2) / (2 × 2 × 3.14) / (1-3 / 5) ≈ 4.78 (CM)
An applied problem of finding the volume of a cylinder in the sixth grade of primary school
The surface area of a cylinder is 125.6 square centimeters, and the sum of its bottom diameter and height is 10 centimeters. What is the volume of the cylinder?
The result of the formula can not be counted
Let the radius of the bottom be r cm and the radius of the top be h cm
Then 2R + H = 10
2*3.14*R＊R+2*3.14*R*H=125.6
The solutions are: R and H
Volume = 3.14 * r * r * h
Questions and answers about volume
A cuboid glass jar is 8 decimeters long, 4 decimeters high and 2.8 decimeters deep. If a square iron block with 4 decimeters edge length is put in, how many liters of water will overflow from the jar?
(water depth should be 2.5 decimeters?) iron volume = 4 × 4 × 4 = 64 (cubic decimeters) glass tank space = 8 × 6 × (3-2.5) = 24 (cubic decimeters) overflow water volume = iron volume - glass tank space = 64-24 = 40 (cubic decimeters) = 40 (liters). [answer] the water in the tank will overflow 40 liters
RELATED INFORMATIONS
- 1. Party A and Party B want to jointly contract a project. Party A will complete the project within 30 days and Party B will complete the project within 20 days. The contract stipulates that the project will be completed within 15 days. Otherwise, a fine of 1000 yuan will be imposed for each day. Party A and Party B sign the contract after discussion. (1) under normal circumstances, can party A and Party B perform the contract? Why? (2) Now they have cooperated in 75% of the project. Because there is something urgent elsewhere, one person must be transferred. Who is more suitable? Why?
- 2. Calculating volume by double integral V is the sphere x ^ 2 + y ^ 2 + Z ^ 2
- 3. Double integral of basic high number 1.∫∫D（x²-y²)dxdy ,0
- 4. The geometric meaning of double integral is volume, but double integral can produce negative number,
- 5. It is proved that the volume bounded by the tangent plane of any point on the cubic (a > o) of the surface XYZ = A and the three coordinate planes is a certain number The answer is: surface XYZ = A & # 179; the normal direction of (x0, Y0, Z0) is {y0z0, z0x0, x0y0} The tangent plane is: y0z0 (x-x0) + z0x0 (y-y0) + x0y0 (z-z0) = 0 Its intercept on three coordinate axes are 3x0, 3y0 and 3z0 The volume of the tetrahedron bounded by the tangent plane and three coordinate planes is: 27x0y0z0 / 6 = 9A & # / 2 My question is, how do you calculate the intercept above!
- 6. The tangent plane equation at point P (1.1.1)
- 7. Surface x2 + Y2 + Z = 9 tangent plane equation at point 124
- 8. Calculate ∫ ∫ ∑ (x ^ 2 + y ^ 2) ds, where ∑ is the part of paraboloid z = 2-x ^ 2 + y ^ 2 above the xoy plane If ∑ is the entire boundary surface bounded by the cone z = √ (x ^ 2 + y ^ 2) and the plane z = 1, how to find it?
- 9. Find the intersection angle of two curves x + y = 0, XY '= 0 on the surface z = XY The two curves should be x + y = 0, xy = 0
- 10. How to calculate the triple integral of a volume bounded by a rotating paraboloid and a plane perpendicular to the Z-axis in spherical coordinates
- 11. Who can clearly tell me how to calculate double integral Just in contact with two-dimensional random variables in probability theory, it's difficult to be solved by double integral. How can this problem be solved For example, ∫ e ^ - (x + 2Y) x, Y > 0 Is the upper and lower limits x ~ 0,0 Should I separate ∫∫ e ^ - (x + 2Y) into ∫ e ^ - x ∫ e ^ - 2Y and then calculate the integral separately, or should I integrate the e ^ - (x + 2Y) integral again, but if so, there are two variables in it. How should I calculate the integral The upper limit is x and Y. who will write me a specific process The original problem is f (x, y) = AE ^ - (x + 2Y), x, Y > 0, finding constant A. I just want to know the algorithm of this type of problem
- 12. If the curve V is the square of the surface y = x, y = x, x + y + Z = 2, and z = 0 is the defined area, then fffdxdydz =? Calculus
- 13. If the maximum value of the function y = a SiNx + 3cosx + 1 is 6, then a=
- 14. Find the minimum positive period of F (x) = SiNx / 2 quartic power + cosx / 2 quartic power + quarter root sign three times sin2x
- 15. Y = (SiNx + cosx) ^ 2 + 2cosx ^ 2, find the decreasing interval, maximum and minimum
- 16. How to calculate the integral of 1 / ((SiNx + cosx) ^ 2)? RT
- 17. If x is an internal angle of a triangle, then what is the range of the function y = SiNx + cosx? Why 45
- 18. If x is the smallest internal angle in a triangle, then the range of the function y = SiNx + cosx is () A. [12，22]B. （0，32]C. （1，2]D. （12，22]
- 19. Expressing arcsin5 / 13 + arccos (- 3 / 5) with an inverse trigonometric function value I want to ask why the final inverse triangle is expressed in COS instead of sin Is there anything particular about using sin or cos
- 20. Y = 1 + sin (2x) + 2cos ^ 2 (x) = 1 + sin (2x) + 1 + cos (2x) = 2 + sin (2x) + cos (2x) = 2 + √ 2Sin (2x + π / 4), so the period is π =2 + √ 2Sin (2x + π / 4)