Conteúdo principal

Cálculo integral

Lição 1: Comprimento de arco: curvas paramétricas

Comprimento do arco de uma curva paramétrica

Considere a curva parametrizada:

\begin{aligned} x&=\cos(2t) \\\\ y&=6t^{3} \end{aligned}

Qual integral dá o comprimento do arco da curva no intervalo de t, equals, a a t, equals, b?

(Escolha A)
integral, start subscript, a, end subscript, start superscript, b, end superscript, square root of, 4, s, e, n, squared, left parenthesis, 2, t, right parenthesis, plus, 324, t, start superscript, 4, end superscript, end square root, d, t
(Escolha B)
integral, start subscript, a, end subscript, start superscript, b, end superscript, square root of, cosine, squared, left parenthesis, 2, t, right parenthesis, plus, 36, t, start superscript, 6, end superscript, end square root, d, t
(Escolha C)
integral, start subscript, a, end subscript, start superscript, b, end superscript, square root of, cosine, squared, left parenthesis, 2, t, right parenthesis, minus, 36, t, start superscript, 6, end superscript, end square root, d, t
(Escolha D)
integral, start subscript, a, end subscript, start superscript, b, end superscript, square root of, 4, s, e, n, squared, left parenthesis, 2, t, right parenthesis, minus, 324, t, start superscript, 4, end superscript, end square root, d, t

Enroscou?