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Triple integral solving method, device, terminal equipment and readable storage medium
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A technology for triple integrals and storage media, applied to digital differential analyzers, calculations using non-numerical representations, etc., can solve problems such as the inability to automatically identify and calculate triple integrals
Inactive Publication Date: 2020-12-25
WUHAN POLYTECHNIC UNIVERSITY
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[0005] The main purpose of the present invention is to provide a triple integral solving method, device, terminal equipment and readable storage medium, aiming to solve the technical problem that the prior art cannot automatically identify and calculate the triple integral
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example 1
[0199] Example 1 A Case Test of Cartesian Coordinates to Find Triple Integral
[0200] calculate Triple integral on Ω, where Ω is the volume surrounded by the plane x=0, y=0, z=0, x+y+z=1.
[0201] Analyzing the question, it is found that the triple integral can be calculated by any of the 6 computing devices in the Cartesian coordinate method.
[0202] Since Ω is equivalent to: 0≤x≤1, 0≤z≤1-x, 0≤y≤1-x-z. which is Therefore, the information submitted through the input port is shown in Table 1.
[0203] Integrand for triple integral 1 / (x+y+z) 3
the range of variables to integrate first 0≤y≤1-x-z Range of variables for intermediate integrals 0≤z≤1-x variable range for final integration 0≤x≤1
[0204] Information required to be submitted for triple points as shown in Table 1
[0205] Through calculation, the calculation result can be obtained as -5 / 16+1 / 2*log(2).
example 2
[0206] Example 2 A case test of calculating the triple integral with cylindrical coordinates
[0207] Compute the triple integral of ∫∫∫zdxdydz over Ω, where Ω is the surface and z=x 2 +y 2 The enclosed space.
[0208] Since Ω is equivalent to: 0≤t≤2π, 0≤r≤1, which is and x=rcost(t), y=rsin(t). Therefore, the information submitted through the input port is shown in Table 2.
[0209]
[0210] Information required to be submitted for triple points shown in Table 2
[0211] Through calculation, the calculation result can be obtained as 1 / 12π.
example 3
[0212] Example 3 A case test for calculating the triple integral in spherical coordinates
[0213] Calculate ∫∫∫(x 2 +y 2 +z 2 ) triple integral of dxdydz on Ω, where Ω is the plane x 2 +y 2 +z 2 =1 The space body surrounded by .
[0214] Since Ω is equivalent to: y=rsin(a)cos(b), z=rsin(a)sin(b), x=rcos(a), 0≤b≤2π, 0≤a≤π, 0≤r ≤1. which is Therefore, the information submitted through the input port is shown in Table 3.
[0215] Integrand for triple integral x 2 +y 2 +z 2
the range of variables to integrate first 0≤rx≤1 Range of variables for intermediate integrals 0≤a≤π variable range for final integration 0≤t≤2π
[0216] Information required to be submitted for triple points as shown in Table 3
[0217] Through calculation, the calculation result can be obtained as 4 / 5π.
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Abstract
The invention discloses a triple integral solving method and device, terminal equipment and a readable storage medium. The method comprises the steps of firstly calling a preset data interface; and obtaining data to be calculated from the preset data interface, then extracting required target equation parameters from the data to be calculated, then determining a triple integral equation corresponding to the target equation parameters through the target equation parameters, and finally calculating triple integral values of the target equation parameters through the triple integral equation. A unified input interface is designed for solving methods of multiple triple integrals, when the triple integrals need to be calculated, the obtained data can be automatically identified, and corresponding methods are selected from the multiple solving methods for calculation, so that convenience in calculation of the triple integrals is facilitated, and the operation difficulty of a user is reduced.
Description
technical field [0001] The present invention relates to the technical field of triple integral equations, in particular to a triple integral solving method, device, terminal equipment and a readable storage medium. Background technique [0002] With the development of mathematical algorithms, mathematical algorithms play a pivotal role in more and more fields. An algorithm is a specific step in a computation, often used in computation, data processing, and automated reasoning. An algorithm is an accurate and complete description of a solution, a series of clear instructions to solve a problem, and an algorithm represents a systematic method to describe the strategy mechanism for solving a problem. [0003] At present, there are many solving methods for a triple integral. If an input interface is designed for each solving method, this requires the user to choose one of the solving methods for input, and the calculation of the data passed from each interface The process is a...
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