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