Constructing piecewise symbolic function in Matlab

 I am trying to generate a piecewise symbolic function in Matlab. The reason it has to be symbolic is I want to be able to integrate/differentiate the function afterwards and/or insert actual values. I have the following function: 

 

x^3/6   ->   0 < x <= 1
(1/6)*(-3*x^3+12*x^2-12x+4)   ->   1 < x <= 2
(1/6)*(3*x^3-24*x^2+60x-44)   ->   2 < x <= 3
(1/6)*(4-x)^3   ->   3 < x <= 4
0   ->   otherwise 

I am trying to generate a piecewise symbolic function in Matlab. The reason it has to be symbolic is I want to be able to integrate/differentiate the function afterwards and/or insert actual values. I have the following function:

x^3/6   ->   0 < x <= 1
(1/6)*(-3*x^3+12*x^2-12x+4)   ->   1 < x <= 2
(1/6)*(3*x^3-24*x^2+60x-44)   ->   2 < x <= 3
(1/6)*(4-x)^3   ->   3 < x <= 4
0   ->   otherwise

For example, I want to put this function in a variable (let's say f) and then call 

 

 int(diff(f, 1)^2, x, 0, 4) % numbers could be different

and get the (scalar) result 2/3.

I tried various things, involving the piecewise() function and symbolic comparisions, but nothing worked... can you help? :-)  

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Answers: 

One option is to use the heaviside function to make each equation equal zero outside of its given range, then add them all together into one equation: 

 

syms x;
f = (heaviside(x)-heaviside(x-1))*x^3/6 + ...
    (heaviside(x-1)-heaviside(x-2))*(1/6)*(-3*x^3+12*x^2-12*x+4) + ...
    (heaviside(x-2)-heaviside(x-3))*(1/6)*(3*x^3-24*x^2+60*x-44) + ...
    (heaviside(x-3)-heaviside(x-4))*(1/6)*(4-x)^3;
double(int(diff(f, 1)^2, x, 0, 4))

ans =

    0.6667

 

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