Integral dari $$$\cos{\left(y^{2} \right)}$$$

Temukan $$$\int \cos{\left(y^{2} \right)}\, dy$$$.

Integral ini (Integral Kosinus Fresnel) tidak memiliki bentuk tertutup:

$${\color{red}{\int{\cos{\left(y^{2} \right)} d y}}} = {\color{red}{\left(\frac{\sqrt{2} \sqrt{\pi} C\left(\frac{\sqrt{2} y}{\sqrt{\pi}}\right)}{2}\right)}}$$

Oleh karena itu,

$$\int{\cos{\left(y^{2} \right)} d y} = \frac{\sqrt{2} \sqrt{\pi} C\left(\frac{\sqrt{2} y}{\sqrt{\pi}}\right)}{2}$$

Tambahkan konstanta integrasi:

$$\int{\cos{\left(y^{2} \right)} d y} = \frac{\sqrt{2} \sqrt{\pi} C\left(\frac{\sqrt{2} y}{\sqrt{\pi}}\right)}{2}+C$$

$$$\int \cos{\left(y^{2} \right)}\, dy = \frac{\sqrt{2} \sqrt{\pi} C\left(\frac{\sqrt{2} y}{\sqrt{\pi}}\right)}{2} + C$$$A