Fase1_Ejercicios 1-7-12.docx

# Fase1_Ejercicios 1-7-12.docx - 1 x5 x3 f x 2x 2 2 5 3 4 2 x...

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1. x x x x f 2 ) ( 3 5 x 5 + x 3 2 x dx = x 2 ( x 2 + 1 ) 2 dx = ( x 4 2 + x 2 2 ) dx = 1 2 x 4 dx + 1 2 x 2 dx Se aplicala regladela potencia→ x n dx = x n + 1 n + 1 conn = 4 x 4 dx = ¿ x 5 5 ¿ x 2 dx = x 3 3 1 2 x 4 dx + 1 2 x 2 dx = x 5 10 + x 3 6 x 2 ( x 2 + 1 ) 2 dx = x 5 10 + x 3 6 + C 7. ( x + 1 ) dx = xdx + 1 dx x dx→ x 2 2 1 dx→ x x dx + 1 dx = x 2 2 + x → x 2 2 + x + C 12. La integral definida se caracteriza por tener límites de integración superior e inferior, que se reemplazan una vez se haya desarrollado el proceso de integración, teniendo en

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cuenta el siguiente criterio: ), ( ) ( ) ( a F b F dx x f b a generalmente conocido como el Segundo Teorema Fundamental del Cálculo. Evalúe la siguiente integral: 2 2 2 1 ) ( dx x sen ( sen ( x ) + 1 ) 2 dx→ ( sen 2 ( x ) + 2 sen ( x ) + 1 ) dx → sen 2 ( x ) dx + 2
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