$\text { Find the arc length of the graph of the function } y = 8 x ^ { \frac { 3 } { 2 } } + 7 \text { over the interval } [ 0,6 ] \text {. }$
A) $\frac { 865 \sqrt { 865 } - 1 } { 216 }$
B) $\frac { 865 \sqrt { 865 } - 864 } { 216 }$
C) $\frac { 865 \sqrt { 865 } + 1 } { 432 }$
D) $\frac { 865 \sqrt { 865 } + 1 } { 216 }$
E) $\frac { 865 \sqrt { 865 } - 1 } { 432 }$

Question

$\text { Find the arc length of the graph of the function } y = 8 x ^ { \frac { 3 } { 2 } } + 7 \text { over the interval } [ 0,6 ] \text {. }$ 
A) $\frac { 865 \sqrt { 865 } - 1 } { 216 }$
B) $\frac { 865 \sqrt { 865 } - 864 } { 216 }$
C) $\frac { 865 \sqrt { 865 } + 1 } { 432 }$
D) $\frac { 865 \sqrt { 865 } + 1 } { 216 }$
E) $\frac { 865 \sqrt { 865 } - 1 } { 432 }$

Quizplus · Accepted Answer

The correct answer is A because the arc length of the graph of the function $ y = 8 x ^ { \frac { 3 } { 2 } } + 7 $ over the interval $ [ 0,6 ] $ is given by the integral $ \int_0^6 \sqrt{1 + (y')^2} dx $, where $ y' = 12x^{\frac{1}{2}} $. Evaluating this integral gives the answer $ \frac { 865 \sqrt { 865 } - 1 } { 216 }$.