Find the length of the curve. $$y = \frac { 1 } { 6 } \left( x ^ { 2 } + 4 \right) ^ { 3 / 2 } , 0 \leq x \leq 4$$
A) $15.3333$
B) $14.3333$
C) $14.0000$
D) $14.6667$
E) $13.6667$

Question

Quizplus · Accepted Answer

The length of the curve can be found using the formula for arc length: $\int_{a}^{b} \sqrt{1 + \left(\frac{dy}{dx}\right)^2} \, dx$. After finding $\frac{dy}{dx}$ and substituting into the formula, the integral evaluates to approximately 14.6667.

Find the Length of the Curve y=16(x2+4)3/2,0≤x≤4y = \frac { 1 } { 6 } \left( x ^ { 2 } + 4 \right) ^ { 3 / 2 } , 0 \leq x \leq 4y=61​(x2+4)3/2,0≤x≤4

Find the Length of the Curve $y = \frac { 1 } { 6 } \left( x ^ { 2 } + 4 \right) ^ { 3 / 2 } , 0 \leq x \leq 4$