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II. Integration – 3. Generelle områder 208
y
y = 1 + x2 y = 2x 2
1
2
D = {(x,y)| − 1 ≤ x ≤ 1,2x 2 ≤ y ≤ 1 + x 2 }
3.12. Type I ☞ [S] 12.3 Double integrals over general regions
Eksempel 1 - fortsat
1 2
1+x
(x + 2y)dA = (x + 2y)dy dx
D
=
=
−1 2x2 1 2
xy + y
−1
y=1+x 2
y=2x2 dx
1
(x(1 + x
−1
2 ) + (1 + x 2 ) 2 − x(2x 2 ) − (2x 2 ) 2 )dx
1
x