A4-format til udskrift. - Aarhus Universitet

84 II. INTEGRATION
Itereret integral
3 2
0
1
3
x 2 3
y dydx =
0 2 x2 dx
= 3
3 3 x
2 3
= 3 3
2
3
3
= 27
2
2.11. Fortsat avet om ☞ [S] 12.2 Iterated integrals
Eksempel 1 - fortsat
Partial integral
R = [0,3] × [1,2], f(x,y) = x 2 y
A(y) =
=
3
0
= 33
x 3
3 y
x 2 y dx
x=3
x=0
y − 0
3
= 9y
2.12. Sluttelig ens ☞ [S] 12.2 Iterated integrals
Eksempel 1 - fortsat
Itereret integral
2 3
1
0
A(y) = 9y
x 2 y dxdy =
2
1
2 y
= 9
2
= 9( 22
2
= 27
2
0
9y dy
2
1
− 12
2 )
2.13. Test itereret integral ☞ [S] 12.2 Iterated integrals
Test
Lad f(x,y) = xy. Det itererede integral 2 2
xy dxdy er
1 1
(a) 9
2
. (b) 9
4
. (c) 6
4 .
Afkryds den rigtige:
(a) (b) (c)