Give a Definite Integral Representing the Length of the Parametric $x = t ^ { 3 } , y = t ^ { 4 } , 0 \leq t \leq 1$

question 128

Multiple Choice

Give a definite integral representing the length of the parametric curve $x = t ^ { 3 } , y = t ^ { 4 } , 0 \leq t \leq 1$ .

• A) \(\int _ { 0 } ^ { 1 } \left( t ^ { 3 } + t ^ { 4 } \right) d t\)
• B) \(\int _ { 0 } ^ { 1 } \sqrt { t ^ { 3 } + t ^ { 4 } } d t\)
• C) \(\int _ { 0 } ^ { 1 } \sqrt { 1 + 3 t ^ { 2 } } d t\)
• D) \(\int _ { 0 } ^ { 1 } \sqrt { t ^ { 2 } + 4 t ^ { 3 } } d t\)
• E) \(\int _ { 0 } ^ { 1 } \sqrt { 9 t ^ { 4 } + 16 t ^ { 6 } } d t\)
• F) \(\int _ { 0 } ^ { 1 } \sqrt { 4 t ^ { 4 } + 9 t ^ { 6 } } d t\)
• G) \(\int _ { 0 } ^ { 1 } \sqrt { t ^ { 5 } + t ^ { 7 } } d t\)
• H) \(\int _ { 0 } ^ { 1 } \sqrt { 8 t ^ { 6 } + 6 t ^ { 8 } } d t\)

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