I am trying to integrate the following triple integral, which has a heaviside function in the inner most integral:(adsbygoogle = window.adsbygoogle || []).push({});

$$ \frac{16}{c_{4}^{4}} \int_{0}^{c_{4}} c_{3}dc_{3} \int_{c_{3}}^{c_{4}} \frac{dc_{2}}{c_{2}} \int_{0}^{c_{2}}f(x)\left ( 1-H\left ( x-\left ( c_{4}-a \right ) \right ) \right )dx $$

where f(x)=x. I know ##c_{2}>0, c_{3}>0 , c_{4}>0, x>0 , a>0 ,$c_{4}>a##

I get the right answer (which I know already) using symbolic integration and the heaviside function in Matlab, which is:

$$1-4\frac{a^{2}}{c_{4}^{2}}+4\frac{a^{3}}{c_{4}^{3}}-\frac{a^{4}}{c_{4}^{4}}$$

However, it is not clear to me how to do this manually? I would like to know because I need to integrate this numerically for cases where f(x) is a more complicated function.

Many thanks in advance!

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# A Integrating definite Heaviside function

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