Integral sin(x^2) from 0 to infinity

Описание

In this video I use complex analysis to calculate the integral of sin(x^2) from 0 to infinity. Notice that even though sin(x^2) does not have an antiderivative in terms of elementary functions, we can still calculate the integral on the whole half line! There's even a bit of concavity involved!

Update: There's a small typo in this video: With the concavity part, it shouldn't be that cos is below its tangent line (which is still true), but rather that cos is above the secant line connecting the points (0,1) and (1,0), which is y = 1-t so the correct estimate is that cos(pi/2 t) is greater than or equal to 1-t. The rest of the video still proceeds the same. Thanks Tobias for catching that mistake :)