Calculating integral of earths orbit but with visual basic.

[Lengalicious]

Homework Statement

Ok for starters, I wasn't entirely sure whether this was supposed to go under physics or comp sci, this is a 'physics' problem I believe but done through visual basic, anyways.

So I have a program where the Earth is animated to orbit the sun based on Newtons laws, I need to calculate the definite integral from X = start of orbit, to X = 0 ∫ Y(x) dx based on the linear interpolation formula shown below.

Homework Equations

Extended linear interpolation formula: 1/2*(f(x₁) + f(x₂))*h + 1/2*(f(x₃) + f(x₄))*h + . . + 1/2*(f(x_n-1) + f(x_n))*h

where h is supposed to be x₂-x₁ for the 1st term then x₃-x₂ for the next term etc.

The Attempt at a Solution

Please note that before this question I had a question to integrate ∫ 1/R(t)² dt from where the Earth starts to X=0 before the one I'm asking and I achieved this by doing a sum within the While loop, ie.

While x > 0

Sum = Sum + Function

End While

Then taking away the 1/2*(1st + last) terms to adjust for the error in the extended interpolation formula.

Now for the question I'm completely stuck all I can suggest to myself is doing another summation during the loop of the function 'Y' but then I have to somehow adjust the answer so that it gives the same answer as the formula but I don't understand how to multiply each term by 'h' in visual basic? Any suggestions?

 

[mark726]

Hi there,

I would suggest breaking down the problem into smaller steps and tackling them one at a time. First, try to understand the extended linear interpolation formula and how it applies to your problem. Then, try to write out the steps for calculating the integral using the formula. Once you have a clear understanding of the steps, you can start implementing them in your program.

In terms of multiplying each term by "h" in Visual Basic, you can use the "*" operator to multiply two values. For example, if you have a variable "h" and a value "f(x1)", you can write it as "h * f(x1)". You can also use the built-in function "Math.Pow" to raise a value to a power, in this case "h" raised to the power of 2. So you can write it as "Math.Pow(h, 2)".

I hope this helps and good luck with your program!