# Engenheira

263 palavras 2 páginas
Cálculo de integrais do tipo

∫ ( f ⋅ f ) dx αL βL b L

f a L

f
L

b
L

b

b L

b1 L

b2

a ⋅b ⋅ L

1 ⋅ a ⋅b ⋅ L 2 b⋅L ⋅ (a1 + 2 ⋅ a2 ) 6 a ⋅b ⋅ L ⋅ (1 + α ) 6 1 ⋅ a ⋅b ⋅ L 3 1 ⋅ a ⋅b ⋅ L 4 5 ⋅ a ⋅b ⋅ L 12 b⋅L ⋅ (a2 + 2 ⋅ a3 ) 6

1 ⋅ a ⋅b ⋅ L 2 b⋅L ⋅ (2 ⋅ a1 + a2 ) 6 a ⋅b ⋅ L ⋅ (1 + β ) 6 1 ⋅ a ⋅b ⋅ L 3 1 ⋅ a ⋅b⋅ L 12 1 ⋅ a ⋅b ⋅ L 4 b⋅ L ⋅ (a1 + 2 ⋅ a3 ) 6

a⋅L ⋅ (b1 + b2 ) 2
L ⋅ (2 ⋅ a1 ⋅ b1 + a1 ⋅ b2 + a2 ⋅ b1 + 2 ⋅ a2 ⋅ b2 ) 6 a⋅L ⋅ [(1 + β ) ⋅ b1 + (1 + α ) ⋅ b2 ] 6 1 ⋅ a ⋅ L ⋅ (b1 + b2 ) 3 a⋅L ⋅ (b1 + 3 ⋅ b2 ) 12 a⋅L ⋅ (3 ⋅ b1 + 5 ⋅ b2 ) 12 L ⋅ [a1 ⋅ b1 + a2 ⋅ b2 + 2 ⋅ a3 ⋅ (b1 + b2 )] 6

1 ⋅ a ⋅b ⋅ L 2 b⋅L ⋅ [(1 + β ) ⋅ a1 + (1 + α ) ⋅ a2 ] 6 1 ⋅ a ⋅b ⋅ L 3 a ⋅b ⋅ L ⋅ (1 + α ⋅ β ) 3 a ⋅b ⋅ L ⋅ 1+α +α 2 12

a1 L

a2

b⋅L ⋅ (a1 + a2 ) 2 1 ⋅ a ⋅b ⋅ L 2
*

αL a L

βL

a L

2 ⋅ a ⋅b ⋅ L 3 1 ⋅ a ⋅b ⋅ L 3 2 ⋅ a ⋅b ⋅ L 3 b⋅L ⋅ (a1 + a2 + 4 ⋅ a3 ) 6

tangente

a L

*

(

) )

tangente

a L
L/2 a1 a3 L a2

*

a ⋅b ⋅ L ⋅ 5− β − β 2 12

(

*

∫ ( f ⋅ f ) dx
FEUP

* parábola de segundo grau

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