Getting complex value for real integration

2 次查看（过去 30 天）

Mithun Kumar Munaganuri 2022-3-31

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1685254-getting-complex-value-for-real-integration

评论： Mithun Kumar Munaganuri 2022-4-5

I'm getting complex value in real integration while trying to find area under ellipse as shown in below figure. Please advise

9 个评论
显示 7更早的评论隐藏 7更早的评论

Mithun Kumar Munaganuri 2022-4-4

@Steven Lord Yes, I'm trying to find the area bounded by a portion of the ellipse. Lengths of minoand major axes of the ellipse are 2a,2b respectively. Equation that generates this ellipse is provided below the picture drawn.

@Torsten I was able to find the area after taking some assumptions and modifying the code.

Mithun Kumar Munaganuri 2022-4-4

@Torsten and @Steven Lord Thanks for your help, I'm able to find the required area after specifying some assumptions and simplifying the equation.

请先登录，再进行评论。

请先登录，再回答此问题。

采纳的回答

David Goodmanson 2022-4-4

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1685254-getting-complex-value-for-real-integration#answer_934069

编辑：David Goodmanson 2022-4-4

在 MATLAB Online 中打开

Hi Mithun,

One of the more straightforward methods is to forget about symbolics and just write down the solution for y. The ellipse has semimajor axis a along x, semiminor axis b along y, and is centered at

( w/2, -(b/(2*a))*sqrt(4*a^2-w^2) )

so that the ellipse passes through both the origin and (w,0). w has to be less than 2*a, the major axis. Solve the ellipse equation for y,

( y + (b/(2*a))*sqrt(4*a^2-w^2) )^2/b^2 = 1 - (x-w/2).^2/a^2 
take the sqrt of both sides**, rearrange
y = -(b/(2*a))*sqrt(4*a^2-w^2) +- b*sqrt((1-(x-w/2).^2/a^2)).

** the sqrt of the left hand side is taken as positive. The sqrt of the right hand side can be either sign, but the positive sqrt is chosen since from the figure, y>=0. So

a = 3; b = 2; w = 5;
fun = @(x) -(b/(2*a))*sqrt(4*a^2-w^2) + b*sqrt((1-(x-w/2).^2/a^2));
integral(fun,0,w) 
   ans = 3.1468

3 个评论
显示 1更早的评论隐藏 1更早的评论

David Goodmanson 2022-4-4

Hi Mithun,

you're most welcome. One thing I forgot to mention is that when you post a question it's not best practice to post images of code. It's much better to copy in the code as text. That way, people looking to assist can just copy the code and run it, rather than having to type it in by hand.

Mithun Kumar Munaganuri 2022-4-5