Ejercicios (6) - Gua Semana 6 Ingeniera Matematica FACULTAD...

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Ingenier´ ıa Matem´ atica Universidad de Chile Gu´ ıa Semana 6 Ingenier´ ıa Matem´atica FACULTAD DE CIENCIAS F ´ ISICAS Y MATEM ´ ATICAS UNIVERSIDAD DE CHILE C´alculo Diferencial e Integral 08-2 Ejercicios 1. Sea R una funci´on racional en la cual aparecen s´ olo sen x y cos x . Escribir la integral i R (sen x, cos x ) dx usando el cambio de variable u = tan( x/ 2). 2. Usando integraci´ on por partes calcule las siguientes primitivas (a) i x sen( x ). (b) i x cos( x ). (c) i xe x . (d) i x senh( x ). (e) i x cosh( x ). (f) i x 1 + x 2 . (g) i x x 2 - 1 . (h) i x 2 sen( x ). (i) i x 2 cos( x ). (j) i x 2 e x . (k) i x 2 senh( x ). (l) i x 2 cosh( x ). (m) i x 2 1 + x 2 . (n) i x 2 x 2 - 1 . 3. Establezca f´ormulas de recurrencia para la expresi´ on I n , dada por (a) I n = i x n sen( x ). (b) I n = i x n cos( x ). (c) I n = i x n e x . (d) I n = i sen n ( x ). (e) I n = i cos n ( x ). I n = i x n sinh(2 x ). 4. Utilizando integraci´ on de funciones racionales calcule las siguientes primitivas (a) i 1 1 + x . (b) i 1 x 2 + 2 x + 1 .
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