Integrais duplos e de linha

20 Integrais Duplos
1.4 Integrais duplos - Exercícios propostos
1. Determine as expressões gerais das primitivas para as funções:
(a) f(x, y) =x 3 +6y 2 − 5xy 2 − 10x 2 y 3
(b) f(x, y) = ¡ x2 + y ¢ 4
x
(c) f(x, y) = y
x + y2 (d) f(x, y) = 10y
x 2 − 9
(e) f(x, y) = x3 + y 2
x 2 + y 2
1
(f) f(x, y) = q
4 − (x + y) 2
(g) f(x, y) =
10
3x + y 2
(h) f(x, y) =20 ¡ x 2 − y 2¢ −1
(i) f(x, y) =lnx + y
³
(j) f(x, y) =ln 2x + y
´
3
(k) f(x, y) = 10
x 2 − y 2
(l) f(x, y) =
x
(x 2 + y) 4
(m) f(x, y) = 2y
x2 − 16
(n) f(x, y) = p 4x − y2 (o) f(x, y) = arctan (x + y)
(p) f(x, y) =sin 2 (3x + y)
2. Mostre que
Z Ã
2 Z 2x2 1
x
(x 3 +2y)dy
!
dx = 559
15 .