Set Up an Integral for the Length of the Curve $$y = \sqrt { 1 - x ^ { 8 } } , - \frac { 1 } { 4 } \leq x \leq \frac { 1 } { 4 }$$

question 133

Multiple Choice

Set up an integral for the length of the curve.
- $$y = \sqrt { 1 - x ^ { 8 } } , - \frac { 1 } { 4 } \leq x \leq \frac { 1 } { 4 }$$

• A) \(\int _ { - 1 / 4 } ^ { 1 / 4 } \sqrt { \frac { 5 - 4 x ^ { 8 } } { 4 \left( 1 - x ^ { 8 } \right) } } d x\)
• B) \(\int _ { - 1 / 4 } ^ { 1 / 4 } \sqrt { \frac { 4 + 64 x ^ { 14 } } { 4 } } d x\)
• C) \(\int _ { - 1 / 4 } ^ { 1 / 4 } \sqrt { \frac { 4 - 4 x ^ { 8 } + 8 x ^ { 7 } } { 4 \left( 1 - x ^ { 8 } \right) } } d x\)
• D) \(\int _ { - 1 / 4 } ^ { 1 / 4 } \sqrt { \frac { 4 - 4 x ^ { 8 } + 64 x ^ { 14 } } { 4 \left( 1 - x ^ { 8 } \right) } } d x\)

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