Tag Archives: symmetry

One cute integral served two ways

Research kicks up, writing kicks back. So in this brief note, we examine a pair of methods to examine an integral. They’re both very clever, I think. We seek to understand $$ I := \int_0^{\pi/2}\frac{\sin(x)}{\sin(x) + \cos(x)} dx $$

We base our first idea on an innocuous-seeming integral identity.

For $latex {f(x)}$ integrable on $latex {[0,a]}$, we have $$ \int_0^a f(x) dx = \int_0^a f(a-x)dx. \tag{1}$$

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