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Integral de $$$\pi \sin{\left(x \right)}$$$
Calculadora relacionada: Calculadora de integrales definidas e impropias
Tu entrada
Halla $$$\int \pi \sin{\left(x \right)}\, dx$$$.
Solución
Aplica la regla del factor constante $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ con $$$c=\pi$$$ y $$$f{\left(x \right)} = \sin{\left(x \right)}$$$:
$${\color{red}{\int{\pi \sin{\left(x \right)} d x}}} = {\color{red}{\pi \int{\sin{\left(x \right)} d x}}}$$
La integral del seno es $$$\int{\sin{\left(x \right)} d x} = - \cos{\left(x \right)}$$$:
$$\pi {\color{red}{\int{\sin{\left(x \right)} d x}}} = \pi {\color{red}{\left(- \cos{\left(x \right)}\right)}}$$
Por lo tanto,
$$\int{\pi \sin{\left(x \right)} d x} = - \pi \cos{\left(x \right)}$$
Añade la constante de integración:
$$\int{\pi \sin{\left(x \right)} d x} = - \pi \cos{\left(x \right)}+C$$
Respuesta
$$$\int \pi \sin{\left(x \right)}\, dx = - \pi \cos{\left(x \right)} + C$$$A