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Integration of a Symmetric Function with a Linear Weight
If:
$$f(a-x)=f(x)$$
then:
$$\int_0^axf(x)\,dx=\frac{a}{2}\int_0^af(x)\,dx$$
Usage
- Very useful for definite integrals involving $$x$$ multiplied by a symmetric function.
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Integration of a Symmetric Function with a Linear Weight
If:
$$f(a-x)=f(x)$$
then:
$$\int_0^axf(x)\,dx=\frac{a}{2}\int_0^af(x)\,dx$$
Usage
- Very useful for definite integrals involving $$x$$ multiplied by a symmetric function.
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