integral de 0 a 3 de sqrt((8t)^23^2) - Symbolab

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04/06/22, 19:57 integral de 0 a 3 de sqrt((8t)^2+3^2) - Symbolab
https://pt.symbolab.com/solver/step-by-step/%5Cint_%7B0%7D%5E%7B3%7D%5Csqrt%7B%5Cleft(8t%5Cright)%5E%7B2%7D%2B3%5E%7B… 1/2
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Solução
Passos
∫ 8t + 3 dt
= ∫ 64t + 9 dt
= ∫
8
9
 sec u du
=
8
9
 ·∫ sec u du
=
8
9
 2
sec u sin u
 + 2
1
 ·∫ sec u du
=
8
9
 2
sec u sin u
 
+
2
1
 
ln 8 + 65
=
8
9
 2
1
 sec u tan u + 2
1
 ln 8 + 65
=
8
9
 4 65 + 2
1
 ln 8 + 65
∫ 8t + 3 dt =
8
9
 
4 65 +
2
1
 
ln 8 + 65 Decimal:     37.84192…
0
3√ ( )2 2 ( √ ( √ ) ) ( )
0
3√ ( )2 2
Simpli�car 8t + 3 : 64t + 9√ ( )2 2 √ 2
0
3√ 2
Aplicar integração por substituição trigonométrica
0
arctan 8( ) 3 ( )
Remover a constante: ∫a · f x dx = a ·∫f x dx( ) ( )
0
arctan 8( ) 3( )
Aplicar a redução de integrais
([ 2( ) ( ) ]arctan 8( )
0 0
arctan 8( )
( ) )
∫ sec u du = ln 8 + 65
0
arctan 8( )
( ) ( √ )
([ 2( ) ( ) ]arctan 8( )
0
( √ ) )
Simpli�car 
8
9
 2
sec u sin u
 + 2
1
 ln 8 + 65 : 8
9
 2
1
 sec u tan u + 2
1
 ln 8 + 65([ 2( ) ( ) ]arctan 8( )0 ( √ ) ) ( [ ( ) ( ) ]arctan 8( )0 ( √
([ ( ) ( ) ]arctan 8( )
0
( √ ) )
Calcular os limites: 4 65√
( √ ( √ ) )
04/06/22, 19:57 integral de 0 a 3 de sqrt((8t)^2+3^2) - Symbolab
https://pt.symbolab.com/solver/step-by-step/%5Cint_%7B0%7D%5E%7B3%7D%5Csqrt%7B%5Cleft(8t%5Cright)%5E%7B2%7D%2B3%5E%7B… 2/2
Grá�co
Plotar o grá�co: 8t + 3 between 0 and 3√ ( )2 2