problems with integration

[Han]

(12-06-2014 01:39 PM)resolved Wrote:  I tried integrating with piecewise in the integral I get "Warning: piecewise indefinite integration does not return a continuous antiderivative" Enter again and I get each term integrated separately. for example I assigned y2 the following function

y2:=-24+18*piecewise(x-9 if x>0, 0 if x<=0) + 3*(piecewise((x-9)^2 if x>0, 0 if x<=0)) + 21*piecewise((x-3) if x>0, 0 if x<=0) - 3*(piecewise((x-3)^2 if x>0, 0 if x<=0))

Why are you defining the piecewise function to break at x=0? Should each piecewise function break at x=9 or x=3?





I entered in the antiderivative as shown in the screens above, and solved with

solve({f(3)=0,f(9)=0},{c1,c2}) and got {[72 -108]}

So the HP Prime knows how to solve the final equation, provided that it's constructed correctly.

The issue here is that you are using a regular antiderivative to compute the antiderivative of <x-a>^k. They aren't technically the same thing because a regular antiderivative of something like (x-a) is correct up to any constant.
\[ \frac{1}{2}(x-a)^2, \quad \frac{x^2}{2}-ax, \quad \frac{x^2}{2}-ax + C, \quad etc \]
On the other hand antiderivative of something like <x-a> must necessarily be 1/2*<x^2-2ax+a^2> + C based on my understanding of your description of <x-a>.

I'm not sure that even mathematica can correctly give you the antiderivative unless it knows how to handle functions of the form <x-a>. Does it? I'm not at my office to test.