Cálculo II - Métodos de Integração

Cálculo II Métodos de Integração Professor Beethoven 1 Calcule as integrais trigonométricas a 𝑐𝑜𝑠3𝑥 𝑠𝑒𝑛 𝑥 𝑑𝑥 b 𝑠𝑒𝑛3𝑥 𝑑𝑥 c 𝑠𝑒𝑛5𝑥 𝑑𝑥 d 𝑐𝑜𝑠3𝑥 𝑑𝑥 e 𝑠𝑒𝑛3𝑥 𝑐𝑜𝑠3𝑥 𝑑𝑥 f 𝑐𝑜𝑠2𝑥 𝑑𝑥 g 𝑠𝑒𝑛7𝑥 𝜋2 0 𝑑𝑥 h 8 𝑠𝑒𝑛4𝑥 𝜋 0 𝑑𝑥 i 16 𝑠𝑒𝑛2𝑥 𝑐𝑜𝑠2𝑥 𝑑𝑥 j 8 𝑐𝑜𝑠32𝑥 sen 2𝑥 𝑑𝑥 k 1cos 𝑥 2 2𝜋 0 𝑑𝑥 l 1 𝑠𝑒𝑛2𝑥 𝜋 0 𝑑𝑥 m 𝑠𝑒𝑐2𝑥 𝑡𝑔 𝑥 𝑑𝑥 n 𝑠𝑒𝑐3𝑥 𝑡𝑔 𝑥 𝑑𝑥 o 𝑠𝑒𝑐2𝑥 𝑡𝑔2 𝑥 𝑑𝑥 p 2 𝑠𝑒𝑐3𝑥 0 𝜋3 𝑑𝑥 q 𝑠𝑒𝑐4𝑥 𝑑𝑥 r 𝑐𝑜𝑠𝑠𝑒𝑐4𝑥 𝜋2 𝜋4 𝑑𝑥 s 4 𝑡𝑔3𝑥 𝑑𝑥 t 𝑐𝑜𝑡𝑔3𝑥 𝜋3 𝜋6 𝑑𝑥 u 𝑠𝑒𝑛 3𝑥 𝑐𝑜𝑠 2𝑥 𝑑𝑥 v 𝑠𝑒𝑛 3𝑥 𝑠𝑒𝑛 3𝑥 𝜋 𝜋 𝑑𝑥 w 𝑐𝑜𝑠 3𝑥 𝑐𝑜𝑠 4𝑥 𝑑𝑥 x 𝑠𝑒𝑐3𝑥 𝑡𝑔 𝑥 𝑑𝑥 y 𝑡𝑔2𝑥 𝑐𝑜𝑠𝑠𝑒𝑐 𝑥 𝑑𝑥 z 𝑥 𝑠𝑒𝑛2𝑥 𝑑𝑥 2 Calcule as integrais por substituição trigonométrica a 1 9𝑥2 𝑑𝑥 b 1 4𝑥2 2 2 𝑑𝑥 c 1 9𝑥2 32 0 𝑑𝑥 d 25 𝑥2 𝑑𝑥 e 1 4𝑥249 𝑑𝑥 f 𝑥249 𝑥 𝑑𝑥 3 Calcule as integrais por frações parciais a 1 1𝑥2 𝑑𝑥 b 𝑥4 𝑥25𝑥6 𝑑𝑥 c 𝑥 𝑥22𝑥3 8 4 𝑑𝑥 d 1 𝑥3𝑥22𝑥 𝑑𝑥 e 𝑥3 𝑥22𝑥1 1 0 𝑑𝑥 f 1 𝑥212 𝑑𝑥 g 1 𝑥1𝑥21 1 0 𝑑𝑥 h 𝑥22𝑥1 𝑥212 𝑑𝑥 i 2𝑥2 𝑥21𝑥13 𝑑𝑥 j 𝑥2𝑥2 𝑥31 𝑑𝑥 k 𝑥2 𝑥41 𝑑𝑥 l 2𝑥35𝑥28𝑥4 𝑥213 𝑑𝑥 m 2𝑥32𝑥21 𝑥2𝑥 𝑑𝑥 n 9𝑥33𝑥1 𝑥3𝑥2 𝑑𝑥 4 Calcule as integrais impróprias a 𝑑𝑥 𝑥 1 0 e 𝑥 𝑙𝑛 𝑥 𝑑𝑥 1 0 b 2𝑥𝑑𝑥 𝑥212 f 𝑑𝑥 𝑥21 0 c 𝑥 0 𝑒𝑥𝑑𝑥 g 𝑑𝑥 𝑥23 1 1 d 𝑑𝑥 1𝑥2 1 0 h 2𝑑𝑥 𝑥21 2 Respostas 1 a 1 4 𝑐𝑜𝑠4𝑥 𝑘 b 1 3 𝑐𝑜𝑠3𝑥 𝑐𝑜𝑠 𝑥 𝑘 c cos 𝑥 2 3 𝑐𝑜𝑠3𝑥 1 5 𝑐𝑜𝑠5𝑥 𝑘 d 𝑠𝑒𝑛 𝑥 1 3 𝑠𝑒𝑛3𝑥 𝑘 e 1 4 𝑠𝑒𝑛4𝑥 1 6 𝑠𝑒𝑛6𝑥 𝑘 f 1 2 𝑥 1 4 𝑠𝑒𝑛 2𝑥 𝑘 g 16 35 h 3𝜋 i 4𝑠𝑒𝑛 𝑥 𝑐𝑜𝑠3𝑥 2 cos 𝑥 𝑠𝑒𝑛 𝑥 2𝑥 𝑘 j 𝑐𝑜𝑠4 2𝑥 𝑘 k 4 l 2 m 1 2 𝑡𝑔2𝑥 𝑘 n 1 3 𝑠𝑒𝑐3𝑥 𝑘 o 1 3 𝑡𝑔3𝑥 𝑘 p 23 ln2 3 q 2 3 𝑡𝑔 𝑥 1 3 𝑠𝑒𝑐2𝑥 𝑡𝑔 𝑥 𝑘 r 4 3 s 2𝑡𝑔2 𝑥 2 ln1 𝑡𝑔2𝑥 𝑘 t 4 3 ln 3 u 1 10 cos 5𝑥 1 2 cos 𝑥 𝑘 v 𝜋 w 1 2 sen 𝑥 1 14 sen 7𝑥 𝑘 x sec 𝑥 ln 𝑐𝑜𝑠𝑠𝑒𝑐 𝑥 𝑐𝑜𝑡𝑔 𝑥 𝑘 y cos 𝑥 sec 𝑥 𝑘 z 1 4 𝑥2 1 4 𝑥 sen 2𝑥 1 8 cos 2𝑥 𝑘 2 a ln 9 𝑥2 𝑥 𝑘 b 𝜋 4 c 𝜋 6 d 25 7 𝑠𝑒𝑛1 𝑥 5 𝑥25𝑥2 2 𝑘 e 1 2 ln 2𝑥 7 4𝑥249 7 𝑘 f 7 𝑥249 7 𝑠𝑒𝑐1 𝑥 7 𝑘 3 a 1 2 ln 1 𝑥 ln 1 𝑥 𝑘 b 1 7 ln𝑥 62𝑥 15 𝑘 c ln 15 2 d 1 2 ln𝑥 1 6 ln𝑥 2 1 3 ln𝑥 1 𝑘 e 3 ln 2 2 f 1 4 ln 𝑥1 𝑥1 𝑥 2𝑥21 𝑘 g 𝜋2 ln 2 8 h 𝑡𝑔1𝑥 1 𝑥21 𝑘 i 𝑥 12 𝑥 11 𝑡𝑔1𝑥 𝑘 j 2 3 ln𝑥 1 1 6 ln𝑥2 𝑥 1 3 𝑡𝑔1 2𝑥1 3 𝑘 k 1 4 ln 𝑥1 𝑥1 1 2 𝑡𝑔1𝑥 𝑘 l 1 𝑥22𝑥2 ln𝑥2 2𝑥 2 𝑡𝑔1𝑥 1 𝑘 m 𝑥2 ln 𝑥1 𝑥 𝑘 n 9𝑥 2 ln 𝑥 1 𝑥 7 ln 𝑥 1 𝑘 4 a 2 b 0 c 1 d 𝜋2 e 14 f π2 g 6 hln 3