Contour and fresnel integrals

Reference no: EM13128740

We want to calculate the integral of the function x*sin(x^4), from 0 to infinity.

We may think that this is similar to a Fresnel Integral (sin(x^2)). In that case, we would set z=e^(iz)^2, and then integrate over the special contour with regions I: 0 to R, II: theta = 0 to pi/4 and then finally to region III: R to 0 along e^i*pi/4. Now, this leads to the problem of integrating the function x*e^(i*x)^4.

A much simpler approach is suggested.

Reference no: EM13128740

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