Integration without using integration

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In summary, the conversation discusses a problem with integrating a formula into an Excel sheet. The formula involves a double integration and the speaker suggests using a Monte Carlo approach as an alternative method, explaining that it involves finding the volume of a 3D shape by generating random points and finding the average function values at those points. The accuracy of the solution depends on the number of points used.
  • #1
isabella
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i'm having a problem with this integration formula..
f=(double integration cos a cos b)/(pi*d^2)dA

i have to insert this formula into an excel sheet but in excel to do integration i need to use an alternative way as the vba codes does not provide any formula for integration.
 
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  • #2
What's the area of integration bounded by?
 
  • #3
the boundary can be set on our own.
 
  • #4
i mean it depends on the area that i chose (dA).i was told that this involves a summation of the values of F.the whole area is divided into many small areas(dA).
 
  • #5
hello isabella

well to me a great way to do integration without using integration is most likely through a monte carlo approach, since we are dealing with double integrals we are trying to find the volume of a 3D shape, the Area you are talking about sounds like the base of this 3D shape now if you generated randomly distributed points over this area, and found the average of the function values at all these points and multiply it by the area of the base you will indeed find the solution to the double integral which is the volume of the 3 dimensional shape, but see this will all be based upon approximations and the more points you use the more accurate you anwser will be

steven
 

FAQ: Integration without using integration

What is integration without using integration?

Integration without using integration is the process of finding the area under a curve without using traditional integration techniques. It involves using other methods, such as geometric reasoning or numerical approximation, to estimate the area.

Why would someone want to use integration without integration?

There are a few reasons someone may want to use integration without integration. One reason is that traditional integration techniques can be complex and time-consuming, so using alternative methods can be more efficient. Another reason is that some functions may not have a closed-form antiderivative, making traditional integration impossible.

What are some common methods for integration without using integration?

Some common methods for integration without using integration are geometric reasoning, such as using rectangles or trapezoids to estimate the area, and numerical approximation methods, such as the trapezoidal rule or Simpson's rule. Other methods include using known integrals or using the properties of integrals to simplify the problem.

Is integration without using integration as accurate as traditional integration?

The accuracy of integration without using integration depends on the specific method used and the level of precision desired. In general, numerical approximation methods can provide accurate estimates, but geometric reasoning methods may introduce some error. However, with careful calculations and a sufficient number of intervals, integration without using integration can be just as accurate as traditional integration.

Can integration without using integration be used for any type of function?

Integration without using integration can be used for many types of functions, but it may not be suitable for all functions. For example, if a function has a highly irregular shape, geometric reasoning methods may not provide accurate estimates. Additionally, some functions may require more complex methods, such as using Fourier series or analytic continuation, to find the area under the curve.

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