Green's function for a boundary value problem

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Nipon
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Homework Statement


I try to integral as picture 1.
The result that is found by me, it doesn't satisfy Green's function for boundary value problem.

Homework Equations

The Attempt at a Solution


show in picture 2 & picture 3.
 
Attachments
  • Handwritten piecewise function G(x,t): equals -cos t sin x for 0 ≤ x ≤ t, and -sin t cos x for t ≤ x ≤ π/2. Below it, r(x) = 1 + x, and the integral from 0 to π/2 of G(x,t) r(t) dt = ?
    1.jpg
    18.9 KB · Views: 396
  • Handwritten calculus working on paper: an integral from 0 to pi/2 of G(x,t) split into two integrals, then the integral from 0 to x of (-cos t + t sin x)(sin t) dt evaluated step by step to sin x [-sin x - x sin x - cos x + 1].
    2.jpg
    26.7 KB · Views: 372
  • Handwritten calculus working on paper: integral from x to pi/2 of G(x,t) sin t dt expanded to cosx times integrals of -sin t and (-sin t - t sin t), evaluated at pi/2 and x, followed by a second line simplifying with sin^2 x + cos^2 x terms to y(x) = -1 - x + sin x - cos x.
    3.jpg
    32.1 KB · Views: 367
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Welcome to the PF :smile:

@Nipon -- we strongly prefer that you post using LaTeX math notation (see INFO, Help/How-To at the top of the page for a tutorial), but we are rounding up some help for you on this first post of yours. You have shown a lot of effort, which is the primary thing that we look for here. Posting your work in images is problematic for a number of reasons, though, so if you get a chance before there are more replies, it would be great if you could look over the LaTeX tutorial, and add a reply with the problem statement and your work in LaTeX notation. Thanks.
 
Upon further review, we will need this to be re-posted as a new thread using LaTeX notation. Just one example of a problem is what you are trying to say with "G" notation? Please read through the LaTeX tutorial thread and start a new thread with your question. Feel free to send me a message if you have questions about how to post (click on my avatar and select Start a Conversation). Thanks! :smile:

Handwritten piecewise function G(x,t) defined as -cos(t)sin(x) for 0 ≤ x ≤ t and -sin(t)cos(x) for t ≤ x ≤ π, followed by r(x) = 1 + x and the integral from 0 to π of G(x,t) r(t) dt = ?.
 
Attachments
  • Handwritten piecewise function G(x,t) defined as -cos(t)sin(x) for 0 ≤ x ≤ t and -sin(t)cos(x) for t ≤ x ≤ π, followed by r(x) = 1 + x and the integral from 0 to π of G(x,t) r(t) dt = ?.
    upload_2018-12-10_17-31-44.png
    17.3 KB · Views: 441