I wanted to know is this true for an even function $\mathbf f(x)$:
$\int_a^b$$\mathbf f(x)$ $\mathbf =$$\int_b^a$$\mathbf f(x)$
That is, there is no requirement of a negative sign while interchanging the limits of integration.
2026-02-23 22:18:00.1771885080
Interchanging limits of integration for an even function
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No, it is not true, since, by definition, if $b<a$, then $\displaystyle\int_b^af(x)\,\mathrm dx=-\int_a^bf(x)\,\mathrm dx$.