What set of reflections would carry triangle ABC onto itself?
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I'll assume you're supposed to compute the line integral of over the given path
. By the fundamental theorem of calculus,
so evaluating the integral is as simple as evaluting at the endpoints of
. But first we need to determine
given its gradient.
We have
Differentiating with respect to gives
and we end up with
for some constant . Then the value of the line integral is
.