INTEGRACIN DEFINIDA
72
5
72
5
-
60
5
72
1
72
1
-
p
-
2
p
-
2
p
4
p
4
p
-
2
3
32
u
2
3
2
u
(
Actividades y Ejercicios
Desarrolla:
1-2 dx = -1 -1 = -1/2 1 _ 1 = -5
(x-1)3 2(x-1)2 -2 (-2)2 (-3)2 72
EMBED Equation.3 b) EMBED Equation.3 c) EMBED Equation.3 d)
EMBED Equation.3 e) EMBED Equation.3
0 sen3x dx = 0 (1-cos2x/2)dx = (x/2-1/4sen2x)0 = /2
EMBED Equation.3 b) EMBED Equation.3 c) EMBED Equation.3 d)
EMBED Equation.3 e) EMBED Equation.3
Calcular el rea del recinto limitado por la curva y = 4x x2y el
eje OX.
En primer lugar se halla los puntos de corte con el eje OX para
representar la curva y conocer los lmites de integracin.
0=4x-x2x=0x=4
En segundo lugar se calcula la integral:
A = 40 (4x-x2)dx = [2x2-x3/3]40 = 32/3u2
EMBED Equation.3 b) EMBED Equation.3 c) EMBED Equation.3 d)
EMBED Equation.3 e) EMBED Equation.3
Hallar el volumen del tronco de cono engendrado por la rotacin
alrededor OX del rea limitada por y = 6 x, y = 0, x = 0, x = 4.
EMBED Equation.3 b) EMBED Equation.3 c) EMBED Equation.3 d)
EMBED Equation.3 e) EMBED Equation.3
Encuentre la longitud del arco de la curva EMBED Equation.3 del
origen al punto EMBED Equation.3
L = 30 1+xdx = 21 t(2t)dt = 21 2t2dt = 2 21 t2dt
L = 2(t3/3)21
L = 2[(8/3)-(1/3)]
L = 2(7/3)
L = 14/3u
EMBED Equation.3 b) EMBED Equation.3 c) EMBED Equation.3 d)
EMBED Equation.3 e) EMBED Equation.3
2
5
32
u
2
3
32
u
-
2
3
16
u
3
3
108
u
3
3
98
u
3
3
308
u
3
3
208
u
3
208
u
3
2
4
9
x
y
=
(
)
3
2
;
3
u
3
11
u
3
14
u
3
16
u
3
4
u
5
14
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