Mathematica [Mathematica] NIntegrate Piecewise function with DE solution

[jackmell]

Hi,

I'd like to solve a DE, create a function with the solution, then use that solution in a Piecewise function, and then NIntegrate the Piecewise function but I can't get NIntegate to work. Here's what I'm trying to do:

mysol = NDSolve[{y'[x] == x, y[0] == 1}, y, {x, 0, 1}]
myy[x_] := Evaluate[y[x] /. mysol];

myf[x_] := Piecewise[{{myy[x], 0 < x <= 1}, {x^2, x > 1}}];

NIntegrate[myf[x], {x, 0, 2}]

NIntegrate then tells me it's not numeric in the interval.

Can someone explain to me what I'm doing wrong?

Thanks,
Jack

 

[phyzguy]

The output of NDSolve (mysol) is a list. You need to take the first element of it in your myy function definition, as follows:

In[25]:= mysol = NDSolve[{y'[x] == x, y[0] == 1}, y, {x, 0, 1}]

In[26]:= myy[x_] := Evaluate[y[x] /. mysol][[1]];

In[27]:= myf[x_] := Piecewise[{{myy[x], 0 < x <= 1}, {x^2, x > 1}}];

In[28]:= NIntegrate[myf[x], {x, 0, 2}]

Out[28]= 3.5

 

[jackmell]

The output of NDSolve (mysol) is a list. You need to take the first element of it in your myy function definition, as follows:

In[25]:= mysol = NDSolve[{y'[x] == x, y[0] == 1}, y, {x, 0, 1}]

In[26]:= myy[x_] := Evaluate[y[x] /. mysol][[1]];

In[27]:= myf[x_] := Piecewise[{{myy[x], 0 < x <= 1}, {x^2, x > 1}}];

In[28]:= NIntegrate[myf[x], {x, 0, 2}]

Out[28]= 3.5

Ok. Thanks a bunch. It's working now. :)