Can we integrate:(adsbygoogle = window.adsbygoogle || []).push({});

$$\int_a^b |x| dx$$

using an antiderivative of ##|x|##, namely ##\frac{1}{2} x |x|##, instead of splitting up the integration interval?

I know this is not particularly useful for integrals such as:

$$\int_{-5}^5 |t^3 - 8| dt$$

However, for absolute value functions with linear arguments, this method (if valid) would be much more efficient.

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# Definite integral of an absolute value function

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