Solve equation that includes integral with variable upper limit.

quadgk((1./(1000.*sqrt(2.*pi))).*(y-x-100).*exp(-((x-150).^2)./200),y-200,y-100)+quadgk((1./(10.*sqrt(2.*pi))).*(exp(-((x-150).^2)./200)),-inf,y-200)=0.53

How to solve the above equation? I want know the value of y.

I can not use fzero function. Please help me. Thanks!

[Walter Roberson]

Are there any other functions that you are not permitted to use besides fzero()?

Are you permitted to use the symbolic toolbox?

Your reference to quadgk suggests that you are using an older version of MATLAB. Which release are you using?

[Daniel Bridges]

Have you tried searching the documentation?

[GUO ZHONG]

Thanks!

Answer 1

[Walter Roberson]

FUN = @(Y)arrayfun(@(y)quadgk(@(x)(1./(1000.*sqrt(2.*pi))).*(y-x-100).*exp(-((x-150).^2)./200),y-200,y-100)+quadgk(@(x)(1./(10.*sqrt(2.*pi))).*(exp(-((x-150).^2)./200)),-inf,y-200),Y)

Now find the zeros of FUN - 0.53

Be careful, though: there gets to be a lot of numeric error beyond about 750.

[GUO ZHONG]

Thanks！ I got the result.^_^

[Weijian Yan]

How did you get the result? Can you show us some detail steps?Thank you!

[Walter Roberson]

Weijian Yan, are you not permitted to use fzero() either, the way the original poster was not permitted for unknown reasons?