Inte!ales
Integrales dobles (áreas)
1. Me dan el dominio.
-1 2.4
X
y
SS, (x y)axay
+
(?)?(x
=
y) axay
+ =
I" 2 yx ay +
=
1 4y3-Efy ay=1,
3
2 +34 -
I-y ay
=
1 cu +
zy) dy
=4y 242
+ 16 16
=
+
-
8 -
4 20.
=
2. chando me dan recinto
A 3x,yEIR
=
ex x)
Dónde corta
a y x
=
2
x
=
X 0
=
x2 -
x 0 =
-
x(X -
1) 3 =
X 1
=
Sa(x y)axdy
+ fc(X
=
-
(x y)ayax
+
(xy
=
Y],,ax
+
=
1 xx +
2 -
(xx Eax (cx 2
+
=
+ -
x3 -
ax 5 5 4 4].
=
+
- -
3
5 5 5 f 20 10 15 6
5
-
+ -
=
20
- -
+ = =
=
68
3. Pelares
Y
2
A 20xy =12
=
x y
+
·Necesario circunferencia.
dydx=13/dAdr x,y) - (r,A)
3 -COSA
X rcDS A
⑧ -rSent r
=
= =
Y
r sen s rsent A
e
rCOS
y
=
Integrales dobles (áreas)
1. Me dan el dominio.
-1 2.4
X
y
SS, (x y)axay
+
(?)?(x
=
y) axay
+ =
I" 2 yx ay +
=
1 4y3-Efy ay=1,
3
2 +34 -
I-y ay
=
1 cu +
zy) dy
=4y 242
+ 16 16
=
+
-
8 -
4 20.
=
2. chando me dan recinto
A 3x,yEIR
=
ex x)
Dónde corta
a y x
=
2
x
=
X 0
=
x2 -
x 0 =
-
x(X -
1) 3 =
X 1
=
Sa(x y)axdy
+ fc(X
=
-
(x y)ayax
+
(xy
=
Y],,ax
+
=
1 xx +
2 -
(xx Eax (cx 2
+
=
+ -
x3 -
ax 5 5 4 4].
=
+
- -
3
5 5 5 f 20 10 15 6
5
-
+ -
=
20
- -
+ = =
=
68
3. Pelares
Y
2
A 20xy =12
=
x y
+
·Necesario circunferencia.
dydx=13/dAdr x,y) - (r,A)
3 -COSA
X rcDS A
⑧ -rSent r
=
= =
Y
r sen s rsent A
e
rCOS
y
=
