# How to NIntegrate a result derived from NDSolve?

I have the following code. My requirements are:

1. I want dp at y = h1 for different values of the parameter x. I need a plot x vs. dp (when y = h1) when x is in [0,1]. Besides I need two column values of dp for different x when y = h1.

2. I want a numerical integration using Nintegrate of dp over x from 0 to 1.

3. I want to plot the integral values with the parameter F.

a = 0.7; b = 0.5; d = 1; F = 0; x = 0.1;
h1 = 1 + a Cos[2.0 Pi x];
h2 = -d - b Cos[(2.0 Pi x)];

eqs1 = s''''[y] - s''''''[y] - s''[y] == 0;

sol =
NDSolve[
{eqs1, s[h1] - F/2 == 0, s'[h1] + 1 == 0, s'''[h1] == 0,
s[h2] + F/2 == 0, s'[h2] + 1 == 0, s'''[h2] == 0},
{s}, {y, -1.5, 1.5}]

p1 =
Plot[Evaluate[{s[y]} /. sol], {y, -1.5, 1.5},
PlotRange -> {{-1.5, 1.5}, {-0.5, 0.5}},
PlotStyle -> {Blue},
Frame -> True,
Axes -> False]

dp = Evaluate[{s'''[y]} /. sol]

delp = NIntegrate[dp, {x, 0.0, 1.0}]

• Where did dpdx come from? Commented Apr 1, 2019 at 6:27
• It was a typos. It must be dp. I have edited it. Commented Apr 1, 2019 at 6:31
• I see, you are integrating a third derivative. So, why isn't s''[1] - s''[0] the integral you need? Commented Apr 1, 2019 at 6:43
• This is an simple example. The original Problem is more complex.Thus I need this to implement it into the original Problem. Commented Apr 1, 2019 at 7:37