Explicit integral could not be found.

2 次查看（过去 30 天）
David Yoo
David Yoo 2012-9-26
Hello,
I am trying to get a solution for below problem, which is to evaluate double integrals of function f(x,y) where the first integral boundary is in variable y. Though the explicit integral could not be found, I expect numerical answer still exists; however I don't know how to get that. I tried double and VPA functions but they didn't work.
___________________________________________________________________________
syms x y
f = x^3*exp(1/x^2)*(x^(1/2)/2)^(1/2);
F = int(f,x,0,y);
ans = int(F,y,0,100); ___________________________________________________________________________
Warning: Explicit integral could not be found.
Warning: Explicit integral could not be found.
ans = int(int(x^3*exp(1/x^2)*(x^(1/2)/2)^(1/2), x = 0..y), y = 0..100)
___________________________________________________________________________
VPA(ans)
ans =
numeric::int(numeric::int(x^3*exp(1/x^2)*(x^(1/2)/2)^(1/2), x = 0..y), y = 0..100)

请先登录，再回答此问题。

回答（2 个）

Babak
Babak 2012-9-26
Mathematica finds the indefinite integral of f over x
http://integrals.wolfram.com/index.jsp?expr=x%5E3*exp%281%2Fx%5E2%29*%28x%5E%281%2F2%29%2F2%29%5E%281%2F2%29&random=false
Take this and evaluate it for the boundaries (i.e. x=y and x=0) and subtract the results. this will give you the definite integral from x=0 to x=y then again try to integrate the result over y.
  3 个评论
显示 1更早的评论
David Yoo
David Yoo 2012-9-26
Thank you for the answer. However, is there any way to solve this kind of problem in Matlab?

请先登录，再进行评论。

Matt Fig
Matt Fig 2012-9-26
编辑：Matt Fig 2012-9-26
Are you sure about those limits?
Here is how one would ordinarily solve such a problem numerically. Note I use limits 1-y and 2-10:
fh = @(y) quadl(@(x) x.^3.*exp(1./x.^2).*(x.^(1/2)/2).^(1/2),1,y);
quadv(fh,2,10)
.
.
.
Let's just check the method with an easy problem. Say we want to solve:
int(int(x,0,y),1/2,1)
By simple calculus this is:
int(y^2/2,1/2,1) = 7/48
So in MATLAB
fh = @(y) quadl(@(x) x,0,y);
quadv(fh,1/2,1) % Equal to 7/48 as expected...

类别

在 Help Center 和 File Exchange 中查找有关 Calculus 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by