Flashcards
Calculo AT 3
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- 1Atividade 3 Thiago Suzarte Carlos Henrique29. Calcular o comprimento de arco da curva
dada na forma paramétrica.
X = 2 cost+ 2t sent,
Y= 2 sent - 2t cost,
0 ≤ t ≤ π/2 - 21º Passo: DerivarX= 2 cost+2tsent
X'= -2sent + 2tcost +2 sent
=2tcost
Y= 2 sent - 2t cost
Y'= 2cost -2cost + 2tsent
= 2tsent - 32º Passo: Aplicar a formula de Comprimento de arco de curvas parametrizadas ∫√(x')²+(y')²∫ 0 a π/2 √(2t cost)² + (2t sent)²dt
∫ 0 a π/2 √4t²cos²t + 4t² sen²t dt - 4Continuação∫ 0 a π/2 √4t²(cos²t + sen²t) dt
∫ 0 a π/2 √4t² dt
∫ 0 a π/2 2t dt - 53º Passo: Integrar∫ 0 a π/2 2t dt
2t²/2 dt[ 0 a π/2
2.0²/2 dt = 0 - 6Continuação2t²/2 dt[ 0 a π/2
2(π/2)²/2 dt
(π/2)² dt
π²/4
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- Flashcards on Calculo AT 3, created by Thiago Dias Suzarte on 04/09/2021.
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