6 integral definida
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Transcript of 6 integral definida
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INTEGRAL DEFINIDA
CAPÍTULO 6
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Fórmulas fundamentales de integración
• Antiderivada de f(x):
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• Funciones trigonométricas, trigonométricas inversas:
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Método de sustitución
• Sustitución:
Si: u= g(x)
du= g’(x) dx
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Integración por partes
• Si f y g son funciones derivables, entonces:
Formula de integración por partes
• Si:
u= f(x) y v= g(x)
entonces:
du=f’(x) dx y dv= g’(x) dx
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Integrales trigonométricas
• Integrales trigonométricas: operaciones algebraicas sobrefunciones trigonométricas.
Caso 1: n positivo impar y
– .
– .
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Caso 2: Uno de los exponentes es entero positivo impar
Si n es impar:
Si m es impar:
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Caso 3: Exponentes enteros positivos pares
– .
– .
– .
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Caso 4: n número entero positivo
– .
– .
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Caso 5: n número entero positivo par
– .
– .
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Caso 6: m número entero positivo par
– .
– .
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Caso 7: n número entero positivo impar
– .
– .
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Caso 8: n número entero positivo impar
Integración por partes:
– .
– .
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Caso 9: n número entero positivo impar y m impar
Integración por partes:
– .
– .