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Integral dari $$$\sin{\left(x^{2} \right)}$$$
Kalkulator terkait: Kalkulator Integral Tentu dan Tak Wajar
Masukan Anda
Temukan $$$\int \sin{\left(x^{2} \right)}\, dx$$$.
Solusi
Integral ini (Integral Fresnel Sinus) tidak memiliki bentuk tertutup:
$${\color{red}{\int{\sin{\left(x^{2} \right)} d x}}} = {\color{red}{\left(\frac{\sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2} x}{\sqrt{\pi}}\right)}{2}\right)}}$$
Oleh karena itu,
$$\int{\sin{\left(x^{2} \right)} d x} = \frac{\sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2} x}{\sqrt{\pi}}\right)}{2}$$
Tambahkan konstanta integrasi:
$$\int{\sin{\left(x^{2} \right)} d x} = \frac{\sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2} x}{\sqrt{\pi}}\right)}{2}+C$$
Jawaban
$$$\int \sin{\left(x^{2} \right)}\, dx = \frac{\sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2} x}{\sqrt{\pi}}\right)}{2} + C$$$A