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# antiderivadasTarea 10 (soluci&Atilde;&sup3;n) (1) -...

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Tarea 10 Calcule las antiderivadas indicadas 1. . dx x sen 4 Solución: Tenemos que dx x x dx x dx x sen dx x sen ) 2 cos 4 1 2 cos 2 1 4 1 ( ) 2 cos 2 1 2 1 ( ) ( 2 2 2 2 4 xdx x sen x xdx xdx dx 2 cos 4 1 2 4 1 4 1 2 cos 4 1 2 cos 2 1 4 1 2 2 dx x x sen x ) 4 cos 2 1 2 1 ( 4 1 2 4 1 4 1 xdx dx x sen x 4 cos 2 1 4 1 2 1 4 1 2 4 1 4 1 C x sen x x sen x 4 32 1 8 1 2 4 1 4 1 C x sen x x sen x 4 32 1 8 1 2 4 1 4 1 C x sen x sen x 4 32 1 2 4 1 8 3 Por tanto C x sen x sen x xdx sen 4 32 1 2 4 1 8 3 4 2. . dx x cos 3 Solución: tenemos que dx x x sen dx x x dx x cos ) 1 ( cos cos cos 2 2 3 dx x x sen dx x cos cos 2 C x sen senx 3 3 1 Por tanto C x sen senx xdx 3 3 3 1 cos

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