Double Integral Syntax: WolframAlpha Solver

In summary, the conversation discusses how to correctly evaluate a double integral using various syntax and methods, including the use of vectors. However, it is mentioned that these methods may not always produce accurate results.
  • #1
N_F
6
0
Online integrator: http://www.wolframalpha.com/


[tex]\int \int (x,y,z) \times (x,y,z) \times (x,y,z)[/tex]


[tex]\int_{L1} \int_{L2} (dl1,0,0) \times (dl2,0,0) \times (0,-1,0)[/tex]

What would be correct syntax to evaluate this double integral?



I tried these, but they produce wrong result:

try #1: integral[{l1,0,0} cross {l2,0,0} cross {0,-1,0}, {l1,0,1}, {l2,0,1}]

try #2: integral[l1,0,1] integral[l2,0,1] {l1,0,0} cross {l2,0,0} cross {0,-1,0}
 
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  • #2
Dunno about the vector stuff, but for regular double integrals I've used the following syntax: integrate x^2 * e^y dx dy, x=0..1, y=0..1

edit: however it doesn't seem very smart and in my experience frequently fails even on relatively simple double integrals.
 
  • #3
Lord Crc said:
Dunno about the vector stuff, but for regular double integrals I've used the following syntax: integrate x^2 * e^y dx dy, x=0..1, y=0..1

edit: however it doesn't seem very smart and in my experience frequently fails even on relatively simple double integrals.

That is yet another way to say the same thing, apperantly, but then, I guess, the original result might actually be correct after all. Who is the judge?
 

1. What is a double integral?

A double integral is a type of mathematical operation that is used to calculate the volume under a surface in three-dimensional space. It involves solving two single integrals, one for each variable, to find the total area under the surface.

2. How is the syntax for double integrals written?

The syntax for double integrals is written as ∫∫ f(x,y) dxdy, where f(x,y) is the function being integrated and dxdy represents the variables of integration. In WolframAlpha, the syntax is written as integrate f(x,y) dxdy.

3. What is a WolframAlpha Solver?

A WolframAlpha Solver is a tool that uses the computational power of WolframAlpha to solve mathematical equations and expressions. It can handle various types of problems, including double integrals, and provides step-by-step solutions for a better understanding of the problem.

4. How do I use WolframAlpha to solve a double integral?

To use WolframAlpha to solve a double integral, simply enter the syntax in the search bar or on the homepage. Make sure to include the function being integrated and the variables of integration. WolframAlpha will then provide a step-by-step solution and a numerical answer, if applicable.

5. What are some common uses of double integrals in science?

Double integrals are commonly used in science to calculate the volume under a surface or to find the average value of a function over a given region. They are also used in physics and engineering to calculate moments of inertia and in probability and statistics to determine probabilities and expected values.

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