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Integral de $$$25 \sin{\left(x \right)}$$$
Calculadora relacionada: Calculadora de integrales definidas e impropias
Tu entrada
Halla $$$\int 25 \sin{\left(x \right)}\, dx$$$.
Solución
Aplica la regla del factor constante $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ con $$$c=25$$$ y $$$f{\left(x \right)} = \sin{\left(x \right)}$$$:
$${\color{red}{\int{25 \sin{\left(x \right)} d x}}} = {\color{red}{\left(25 \int{\sin{\left(x \right)} d x}\right)}}$$
La integral del seno es $$$\int{\sin{\left(x \right)} d x} = - \cos{\left(x \right)}$$$:
$$25 {\color{red}{\int{\sin{\left(x \right)} d x}}} = 25 {\color{red}{\left(- \cos{\left(x \right)}\right)}}$$
Por lo tanto,
$$\int{25 \sin{\left(x \right)} d x} = - 25 \cos{\left(x \right)}$$
Añade la constante de integración:
$$\int{25 \sin{\left(x \right)} d x} = - 25 \cos{\left(x \right)}+C$$
Respuesta
$$$\int 25 \sin{\left(x \right)}\, dx = - 25 \cos{\left(x \right)} + C$$$A