how-to-find-the-antiderivative-of-simple-polynomials-variant-.pptx

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1. Cómo hallar la antiderivada de polinomios sencillos

2. Integrales indefinidas En esta sesión informativa exploraremos cómo hallar la antiderivada de funciones polinómicas sencillas . Las antiderivadas, también conocidas como integrales indefinidas , son esenciales en cálculo y proporcionan una forma de invertir el proceso de diferenciación 01 Identifica el polinomio 02 Aplica la regla de la potencia 03 Combina antiderivadas 04 Constante de integración

3. 01. Identifica el polinomio Empieza por identificar la función polinómica de la que quieres hallar la antiderivada. Un polinomio simple es una expresión matemática formada por una suma de términos, cada uno de los cuales contiene un coeficiente constante y una variable elevada a una potencia entera no negativa

4. 2. A plica la regla de la potencia Para hallar la antiderivada de cada término del polinomio, aplica la regla de la potencia para las antiderivadas . La regla de la potencia establece que si tienes un término de la forma x n , donde n es una constante, la antiderivada es (1/(n+1)) * x (n+1) + C , donde C es la constante de la integración Ejemplo Para el término 2x 3 , la antiderivada es (1/4) * x 4 + C Para el término 5x 2 , la antiderivada es (1/3) * x 3 + C

5. 3. C ombina antiderivadas Si el polinomio consta de varios términos , aplica la regla de la potencia a cada término individualmente y luego combina las antiderivadas 3x 2 + 2x + 7 Encuentra la antiderivada de cada término por separado La antiderivada de 3x 2 es (1/3) * x 3 + C La antiderivada de 2x es x 2 + C La antiderivada de 7 es 7x + C Combina las antiderivadas para obtener la antiderivada final: (1/3) * x 3 + x 2 + 7x + C

6. 04. Incluye la constante de integración Constante de integración Ejemplo La antiderivada En cada antiderivada, incluye siempre la constante de integración , denominada C . Esta constante tiene en cuenta el hecho de que puede haber varias antiderivadas que difieran en un valor constante La antiderivada de 3x 2 es (1/3) * x 3 + C , donde C puede ser cualquier constante Siguiendo estos pasos, puedes hallar la antiderivada de funciones polinómicas sencillas. Las antiderivadas desempeñan un papel crucial en el cálculo, ya que te permiten hallar la función original cuando conoces su tasa de variación (derivada)

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