Find the length of the curve. Select the correct answer.
$$x = \frac { y ^ { 4 } } { 8 } + \frac { 1 } { 4 y ^ { 2 } } , 1 \leq y \leq 3$$
A) $10.2222$
B) $25.055$
C) $13.05$
D) $36.05$
E) None of these

Question

Quizplus · Accepted Answer

The length of the curve can be found using the formula for arc length: $\int_{a}^{b} \sqrt{1 + \left(\frac{dx}{dy}\right)^2} \, dy$. Calculating $\frac{dx}{dy}$ and evaluating the integral from $y = 1$ to $y = 3$ gives approximately 10.2222.

Find the Length of the Curve x=y48+14y2,1≤y≤3x = \frac { y ^ { 4 } } { 8 } + \frac { 1 } { 4 y ^ { 2 } } , 1 \leq y \leq 3x=8y4​+4y21​,1≤y≤3

Find the Length of the Curve $x = \frac { y ^ { 4 } } { 8 } + \frac { 1 } { 4 y ^ { 2 } } , 1 \leq y \leq 3$