Question

Considere a função f(x)=x. Calcule o comprimento desta curva entre os pontos x=2 e 3.


A.√2

B.2√2

C.√5

D.√313

Answer 1

Comprimento de arcos de

curvas

$\boxed{\boxed{\mathtt{L=\int\limits_{a}^{b}\sqrt{{(\dfrac{dy}{dx})}^{2}+1}dx}}}$

$\mathtt{y=x\to~\dfrac{dy}{dx}=1}$

$\mathtt{L=\int\limits_{2}^{3}\sqrt{{1}^{2}+1}dx}$

$\mathtt{L=\sqrt{2}\int\limits_{2}^{3}dx}$

$\mathtt{L=\sqrt{2}x\big|_{2}^{3}}$

$\mathtt{L=\sqrt{2}(3-2)}$

$\huge\boxed{\boxed{\mathtt{L=\sqrt{2}~u.c}}}$

$\boxed{\boxed{\mathtt{Alternativa~a}}}$