Question

Link to document inside
I do not understand the intermediate steps that were taken to solve for a constant of an integral.

Answer 1

http://people.whitman.edu/~hundledr/courses/M367/HWSect01_4.pdf

Question 1.4.2 (B)
Where they solve the ODE:
\[u _{xx} = -\frac{ Q }{ K_{0} } = -x \rightarrow u_{x} = -\frac{1}{2}x ^{2}+\frac{1}{6}L^{2}\]

I do not understand where they got:

\[+\frac{1}{6}L^{2}\]

Because if you solve the integral:

\[\int\limits_{0}^{L}u_{xx} dx =\int\limits_{0}^{L}(-x) dx \]

Don't you just get
\[-\frac{x^{2}}{2}+C_{1}\]
Right?

Answer 2

Solved:

http://openstudy.com/invite-signup?token=NFt%2B55DsgHs1SbmRyfJ43A%3D%3D&source=url