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Double integral of basic high number 1.∫∫D（x²-y²)dxdy ,0
1.∫∫D（x²-y²)dxdy =∫(0,π)dx∫(0,sinx)（x²-y²)dy =∫(0,π)dx[x²sinx - (sin³x)/3]=∫(0,π)[x²(-dcosx) + (sin²x)(dcosx)/3]=∫(0,π)[(1-cos²x)(dcosx)/3] - ...
How to determine the integral limit of double integral in Higher Mathematics
How to determine the integral limit of double integral? According to the textbook, if it is X-type, first make a straight line passing through the region D and parallel to the y-axis, and then the minimum value of the projection of the region D on the x-axis is the lower limit of the integral, and the maximum value is the upper limit of the integral
I just don't know what this projection is about?
The integral limit of Y is always determined, but the integral limit of X is not determined
Ask experts to teach me how to determine the integral limit
In fact, the problem of projection comes from using light to irradiate. If you irradiate d with light parallel to the y-axis, you will get the value on the x-axis. To put it simply, do the tangent line of D and perpendicular to the x-axis. I still think that the meaning of light irradiating is more intuitive. Let's think about it
Under what circumstances should high number double integral be divided into regions?
Under what circumstances should the integral region be divided into parts? Why?
This one. If the X-type is used, why should it be divided into two parts? Rt
The expression of the left end function is different on the upper and lower sides of the x-axis, that is, the expression of the length of the integral interval is different at the intersection of the lines parallel to the x-axis
Double integral and multiple integral related content, such as definition, geometric meaning and calculation method!
On the definition of double integral and multiple integral, geometric meaning and calculation method!
Are you from the Department of mathematics? It's more complicated I'll try to talk about integrability first. Double integral and multiple integral are almost the same. In form, they are a numerical function multiplied by differential element (area or volume), and then integrated. So we can use them to calculate mass, and so on
What is the geometric meaning of triple integral?
There is no intuitive geometric meaning, only physical meaning
Is triple integral geometric?
Double is volume, right
The geometric meaning can be to find the volume of an aggregate
Physically, it is the work on the volume after calculating the area, or other physical quantities
From the geometric meaning of integral
Pi / 2, but PI has never appeared from the beginning to the end
How to understand the geometric meaning?
This integral is simple reasoning and does not need calculation?
y=√(1-x^2)
x^2+y^2=1
This is the unit circle, but Y > = 0, so it's only a semicircle
So the integral is the area of the semicircle
Radius is 1, so area = pi / 2
What is the geometric meaning of double integral
If the integrand function is positive in the integral region, the geometric meaning is the volume of the region bounded by the integral surface and the projection plane. If there are positive and negative, it is the volume of the positive region minus the volume of the negative region
What is the geometric meaning of double integral?
It is easy to say that the double integral is volume. We know that the single integral is area, and the double integral is the superposition of numerous single areas, which is volume
Geometric meaning of double integral
The geometric meaning of double integral ∫ ∫ f (x, y) DXDY is the volume of a cylinder with curved top. The bottom of the cylinder is the integral region D, and the top is the surface determined by z = f (x, y). In this problem, z = (a ^ 2-x ^ 2-y ^ 2) represents the upper part of the sphere x ^ 2 + y ^ 2 + Z ^ 2 = a ^ 2, and the bottom is x ^ 2 + y ^ 2 = a ^ 2 on the xoy plane
RELATED INFORMATIONS
- 1. The geometric meaning of double integral is volume, but double integral can produce negative number,
- 2. 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!
- 3. The tangent plane equation at point P (1.1.1)
- 4. Surface x2 + Y2 + Z = 9 tangent plane equation at point 124
- 5. 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?
- 6. 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
- 7. 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
- 8. If the center of the ellipse is the origin, the focus is on the x-axis, the point P is a point on the ellipse, and the projection of P on the x-axis is exactly the origin of the ellipse The center of an ellipse is at the origin, the focus is on the x-axis, P is a point on the ellipse, the projection of P on the x-axis is just the left focus of the ellipse, the line between P and center O is parallel to the line between the right vertex and the upper vertex, and the distance between the left focus and the left vertex is equal to √ 10 - √ 5. Try to find the eccentricity and equation of the ellipse
- 9. Normal equation of curve y = x ^ 3-3x at point (2,2) If the problem, solve!
- 10. Is the hyperbolic paraboloid obtained by y = ax ^ 2 rotating around the X axis? But how to deduce the hyperbolic paraboloid equation? If y = ax ^ 2 rotates around the X axis, we should get √ y ^ 2 + Z ^ 2 = ax ^ 2. Can this equation change to hyperbolic parabolic equation?
- 11. Calculating volume by double integral V is the sphere x ^ 2 + y ^ 2 + Z ^ 2
- 12. 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?
- 13. Using spherical coordinates to calculate triple integral I = ∫∫∫ Z ^ 2dV, where the graph is composed of x ^ 2 + y ^ 2 + Z ^ 2
- 14. 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
- 15. 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
- 16. If the maximum value of the function y = a SiNx + 3cosx + 1 is 6, then a=
- 17. Find the minimum positive period of F (x) = SiNx / 2 quartic power + cosx / 2 quartic power + quarter root sign three times sin2x
- 18. Y = (SiNx + cosx) ^ 2 + 2cosx ^ 2, find the decreasing interval, maximum and minimum
- 19. How to calculate the integral of 1 / ((SiNx + cosx) ^ 2)? RT
- 20. If x is an internal angle of a triangle, then what is the range of the function y = SiNx + cosx? Why 45