Integral de $$$\frac{\theta \sin{\left(1 \right)}}{4}$$$
Calculadora relacionada: Calculadora de Integrais Definidas e Impróprias
Sua entrada
Encontre $$$\int \frac{\theta \sin{\left(1 \right)}}{4}\, d\theta$$$.
Solução
Aplique a regra do múltiplo constante $$$\int c f{\left(\theta \right)}\, d\theta = c \int f{\left(\theta \right)}\, d\theta$$$ usando $$$c=\frac{\sin{\left(1 \right)}}{4}$$$ e $$$f{\left(\theta \right)} = \theta$$$:
$${\color{red}{\int{\frac{\theta \sin{\left(1 \right)}}{4} d \theta}}} = {\color{red}{\left(\frac{\sin{\left(1 \right)} \int{\theta d \theta}}{4}\right)}}$$
Aplique a regra da potência $$$\int \theta^{n}\, d\theta = \frac{\theta^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ com $$$n=1$$$:
$$\frac{\sin{\left(1 \right)} {\color{red}{\int{\theta d \theta}}}}{4}=\frac{\sin{\left(1 \right)} {\color{red}{\frac{\theta^{1 + 1}}{1 + 1}}}}{4}=\frac{\sin{\left(1 \right)} {\color{red}{\left(\frac{\theta^{2}}{2}\right)}}}{4}$$
Portanto,
$$\int{\frac{\theta \sin{\left(1 \right)}}{4} d \theta} = \frac{\theta^{2} \sin{\left(1 \right)}}{8}$$
Adicione a constante de integração:
$$\int{\frac{\theta \sin{\left(1 \right)}}{4} d \theta} = \frac{\theta^{2} \sin{\left(1 \right)}}{8}+C$$
Resposta
$$$\int \frac{\theta \sin{\left(1 \right)}}{4}\, d\theta = \frac{\theta^{2} \sin{\left(1 \right)}}{8} + C$$$A