A4-format til udskrift. - Aarhus Universitet

Eksempel 5
R
sin(x)cos(y)dA =
2. ITERERET INTEGRAL 89
=
=
π
2
0
π
2
0
π
2
π
2
0
cos(y)
sin(x)cos(y)dxdy
π
2
0
sin(x)dx
sin(x)dx dy
π
2
0
0
= [−cos(x)] π
π
2 2
0 [sin(y)] 0
= (−0 − (−1))(1 − 0)
= 1
cos(y)dy
2.28. Opgave ☞ [S] 12.2 Iterated integrals
Øvelse 16
x
R = [0,1] × [0,1], f(x,y) = xe xy
z
2.29. Opgave løst
Øvelse 16
☞ [S] 12.2 Iterated integrals
xe xy 1 1
dA = xe xy dydx
R
0 0
1
= [e
0
xy ] y=1
y=0 dx
1
= (e
0
x − e 0 )dx
= [e x − x] 1
0
= e − 2
2.30. Test Fubini ☞ [S] 12.2 Iterated integrals
Test
Lad f(x,y) = xlny, R = [0,2] ×[1,2]. Der gælder
R xlny dA = 2
0 x dx 2
lny dy. 1
Afkryds:
ja
nej
y