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