Equality Condition for Absolute-Value Inequality

Equality Condition for Absolute-Value Inequality

Equality in:

$$\left|\int_a^bf(x)\,dx\right|\leq\int_a^b|f(x)|\,dx$$

occurs when $$f(x)$$ does not change sign on the interval, apart from isolated zero points.

Usage

- Used to determine when the absolute-value bound is exact.

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