$$\int_0^{\frac{\pi}2}\frac{\sin 2x}{\sqrt{x}}\,dx$$ How to solve this trigonometric integral? I can't find any solutions. Some books suggest to use Fresnel integral. I would be grateful if you could help me out.
2026-02-23 03:49:21.1771818561
Evaluating $\int_0^{\frac{\pi}2}\frac{\sin 2x}{\sqrt{x}}\,dx$
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This integral is related to Fresnel S integral to which you arrive using the change of variable suggested by 7raisen7.
For your problem, the antiderivative is $$\sqrt{\pi } S\left(\frac{2 \sqrt{x}}{\sqrt{\pi }}\right)$$ and the integral $$\sqrt{\pi } S\left(\sqrt{2}\right)=1.2654828001827241355...$$