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Integral dari $$$\frac{\pi x \sin{\left(7 \right)}}{20}$$$
Kalkulator terkait: Kalkulator Integral Tentu dan Tak Wajar
Masukan Anda
Temukan $$$\int \frac{\pi x \sin{\left(7 \right)}}{20}\, dx$$$.
Solusi
Terapkan aturan pengali konstanta $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ dengan $$$c=\frac{\pi \sin{\left(7 \right)}}{20}$$$ dan $$$f{\left(x \right)} = x$$$:
$${\color{red}{\int{\frac{\pi x \sin{\left(7 \right)}}{20} d x}}} = {\color{red}{\left(\frac{\pi \sin{\left(7 \right)} \int{x d x}}{20}\right)}}$$
Terapkan aturan pangkat $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ dengan $$$n=1$$$:
$$\frac{\pi \sin{\left(7 \right)} {\color{red}{\int{x d x}}}}{20}=\frac{\pi \sin{\left(7 \right)} {\color{red}{\frac{x^{1 + 1}}{1 + 1}}}}{20}=\frac{\pi \sin{\left(7 \right)} {\color{red}{\left(\frac{x^{2}}{2}\right)}}}{20}$$
Oleh karena itu,
$$\int{\frac{\pi x \sin{\left(7 \right)}}{20} d x} = \frac{\pi x^{2} \sin{\left(7 \right)}}{40}$$
Tambahkan konstanta integrasi:
$$\int{\frac{\pi x \sin{\left(7 \right)}}{20} d x} = \frac{\pi x^{2} \sin{\left(7 \right)}}{40}+C$$
Jawaban
$$$\int \frac{\pi x \sin{\left(7 \right)}}{20}\, dx = \frac{\pi x^{2} \sin{\left(7 \right)}}{40} + C$$$A