Symmetry Weighted Integral for a Linear Function

Rarely Tested

Symmetry Weighted Integral for a Linear Function

If:

$$f(a-x)=f(x)$$

then:

$$\int_0^a(a-2x)f(x)\,dx=0$$

Usage

- Used when the integrand contains a linear factor multiplied by a function symmetric about $$x=\frac{a}{2}$$.

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