Formulas del calculo integral

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CALCULO INTEGRAL
FORMULAS
• " d u = u + c
• " a d u = a " d u
• " u m d u = u m +1 + c
m + 1
• " ( u ± v ± w ) d x = " u d x ± " v d x ± " w d x
• " d u =L n u +c
u
• " e u d u = e u + c
• "sen u d u = cos u + c
• " cos u d u = sen u + c
• " tan u d u = - L n | cos v | + c
• " ba ( x ) d x = f ( b ) - g (a )|ba
• Integración por partes
" w d v = u v - " v d u
Ejemplos.
• " ( x 2 - 2 x + 4 ) d x = " x 2 d x - " c x d x + " 4 d x = x 2 + 1 - 2 x 2 + 4 x + c
+ 1 2• " " x 2 - 2 x ( 6 x - 6 ) d x
= " ( x 2 - 2 x ) ½ m ( 6 x - 6 ) d x = 3 " u ½ d u = 3 U 3/2 + c = 2 " v 3 + c
v d v 3/2
v = x 2 - 2 x
d v = ( 2 x - 2 ) d x
•" ( 3 x 3 - 9 x 2 ) 5 ( 18 x 2 - 36 x ) d x = ½ " v 5 d v = ½ v 6 + 6
6/1
v = 3x 2 - 9 x 2 = 1/12 v 6 + c
d v = ( 9 x 2 - 18 x ) d x
• "21 ( x 2 - 2 x ) d x = "21 d x - " 21 x 2 d x - " 21 2 x = x 3 - 2 x 2 | 21 = x 2 - x 2 | 21 =
( 2 ) 3 - ( 2 ) 2 - ( 1 ) 3 - ( 1 ) 2
3 3
= 8/3 - 4 - 1/3 + 1 = 8/3 - 12/3 - 1/3 + 3/3 =Hallar el area bajo la curva de la función.
• y = f ( x ) = x 2 - 3 x

A " 30 ( x 2 - 3 x ) d x =
A " 30 x 2 d x - 3 " 30 x d x = x 3 / 3 - 3 x 2 / 2 | 30
A ( 3 )3 / 3 - 3 ( 3 ) 2 /2 - ( 0 3 /3 - 3 ( 0 ) 2 /2 )
A 9 - 27/2 = 18/2 -27/2 =
• " sen 3 x 2 * 2 x d x = 1/3 " sen d v = 1/3 ( - cos ) + c
v = 3 x 2 = -1/3 cos v + c =-1/3 cos 3 x 2 + c
d v = 6 x d x
• " 2 d x = 2 " d x =
x + 8 x + 8
v = x + 8
d v = d x
- 4
1
4
2 x
y´ = x + 1__
" x 2 + 2 x
- 45.84
11.33
x 1 = 6
y 1= 5
Con x = 5 / 3 es máximo
- 2 cot 2 x
= x 3 - x 2 + 4 x + c
3
2 " ( x 2 - 2 x ) 3 + c
= 1/12 ( 3 x 2 - 9 x 2 ) 6 + c
-2 / 3
- 9 /2 v 2
2 Ln | x + 8 | + C
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