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    <p>One option is to use the <a href="http://www.mathworks.com/help/symbolic/heaviside.html" rel="nofollow noreferrer"><code>heaviside</code></a> function to make each equation equal zero outside of its given range, then add them all together into one equation:</p> <pre><code>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 </code></pre> <p>Another alternative is to perform your integration for each function over each subrange then add the results:</p> <pre><code>syms x; eq1 = x^3/6; eq2 = (1/6)*(-3*x^3+12*x^2-12*x+4); eq3 = (1/6)*(3*x^3-24*x^2+60*x-44); eq4 = (1/6)*(4-x)^3; total = int(diff(eq1, 1)^2, x, 0, 1) + ... int(diff(eq2, 1)^2, x, 1, 2) + ... int(diff(eq3, 1)^2, x, 2, 3) + ... int(diff(eq4, 1)^2, x, 3, 4) total = 2/3 </code></pre> <hr> <p><strong>UPDATE:</strong></p> <p>Although it's mentioned in the question that the <a href="https://www.mathworks.com/help/symbolic/piecewise.html" rel="nofollow noreferrer"><code>piecewise</code></a> function didn't work, <a href="https://stackoverflow.com/a/41991115/52738">Karan's answer</a> suggests it does, at least in newer versions. The documentation for <code>piecewise</code> currently says it was introduced in R2016b, but it was clearly present much earlier. I found it in the documentation for the <a href="https://www.mathworks.com/help/symbolic/index.html" rel="nofollow noreferrer">Symbolic Math Toolbox</a> as far back as R2012b, but the calling syntax was different than it is now. I couldn't find it in earlier documentation for the Symbolic Math Toolbox, but it did show up as a function in other toolboxes (such as the Statistics and Spline Toolboxes), which explains its mention in the question (and why it didn't work for symbolic equations at the time).</p>
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    1. COIt should be 60*x.
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    2. CO@Jonas: Thanks. The `12x` needed to be fixed too.
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