Lista3_calculoII_2014_1 - UNIVERSIDADE FEDERAL DE MATO...

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1 UNIVERSIDADE FEDERAL DE MATO GROSSO Campus Universitário do Araguaia Instituto de Ciências Exatas e da Terra Curso: Ciência da Computação Disciplina: Cálculo II Professor: Renato Ferreira da Cruz 3 a Lista de Exercícios 1 Encontre a área da região sombreada. x y 0 (4 , 4) y = x y =5 x - x 2 a) x y 0 y = x +2 y = 1 x +1 x =2 b) x y 0 x = y 2 - 2 x = e y y =1 y = - 1 c) x y 0 x = y 2 - 4 y x =2 y - y 2 ( - 3 , 3) d) x y 0 (2 , 8) ( - 2 , 8) - 2 - 1 1 2 8 y = x 4 - 2 x 2 y =2 x 2 e) x y 0 1 2 1 2 x =2 y x =3 - y x =( y - 1) 2 f)
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2 UNIVERSIDADE FEDERAL DE MATO GROSSO 2 Esboce a região delimitada pelas curvas dadas. Decida quando integrar em relação x ou a y . Então, calcule a área da região. a ) y = x +1 , y =9 - x 2 , x = - 1 e x =2 b ) y =sen x , y = e x , x =0 e x = π 2 c ) y = x e y = x 2 d ) y = x 2 e y = x 4 e ) y = 1 x , y = 1 x 2 e x =2 f ) y = x 2 e y 2 = x g ) y = x 2 e y =4 x - x 2 h ) y =cos x , y =2 - cos x e 0 x 2 π i ) y =tg x , y =sen x e - π 3 x π 3 j ) y = x , y = x 2 e x =9 k ) y =2 y 2 e x =4+ y 2 l ) 4 x + y 2 =12 e x = y m ) x =1 - y 2 , x = y 2 - 1 n ) y = | x | e y = x 2 - 2 o ) y = 1 x , y = x , y = x 4 e x > 0 p ) y =3 x 2 , y
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