11
votes
0answers
71 views
+100
An integral involving Fresnel integrals $\int_0^\infty \left(\left(2\ S(x)-1\right)^2+\left(2\ C(x)-1\right)^2\right)^2 x\ \mathrm dx,$
I need to calculate the following integral:
$$\int_0^\infty \left(\left(2\ S(x)-1\right)^2+\left(2\ C(x)-1\right)^2\right)^2 x\ \mathrm dx,$$
where
$$S(x)=\int_0^x\sin\frac{\pi z^2}{2}\mathrm dz,$$
...
0
votes
1answer
60 views
Evaluating $\int_0^1 \! C(x) \, \mathrm dx$ through integration by parts
$$
\int_0^1 \! C(x) \, \mathrm{d} x.
$$
where $C(x) = \int_0^x \cos(t^2) \, \mathrm{d} t$.
I am really not quite sure how to go about this one, especially given that it needs to be calculated ...
