Find the length of the curve. $x = 3 t ^ { 2 } + 8$ , $y = 2 t ^ { 3 } + 8$ , $0 \leq t \leq 1$
A) $2 \sqrt { 2 } - 2$
B) $4 \sqrt { 2 }$
C) $4 \sqrt { 2 } - 1$
D) $4 \sqrt { 2 } - 2$
E) None of these

Question

Quizplus · Accepted Answer

The length of the curve is found using the formula $ \int_{a}^{b} \sqrt{\left(\frac{dx}{dt}\right)^2 + \left(\frac{dy}{dt}\right)^2} \, dt $. Calculating the derivatives and evaluating the integral from 0 to 1 gives $4 \sqrt{2} - 2$.

Find the Length of the Curve x=3t2+8x = 3 t ^ { 2 } + 8x=3t2+8

Find the Length of the Curve $x = 3 t ^ { 2 } + 8$