Problem with latest XKCD

[Albert Chan]

We can solve definite integral by folding:

\(\int_a^b f(x) \;dx =
\int_a^\frac{a+b}{2} (f(x) + f(a+b-x)) \;dx
\)

∫(x*sin(x)^2, x=0 .. pi) = ∫(x*sin(x)^2 + (pi-x)*sin(x)^2, x=0 .. pi/2) = pi * ∫(sin(x)^2, x = 0 .. pi/2)

We can use integral identities for RHS ... or we just fold again!

pi * ∫(sin(x)^2, x = 0 .. pi/2) = pi * ∫(sin(x)^2 + cos(x)^2, x = 0 .. pi/4) = pi * pi/4 = pi^2/4