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Parametric Arc Length
Worksheet
Grade Level
Calculus II
CAL2.100 Parametric Arc Length
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🔴 Hard
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A differentiable parametric curve has \(x'(t)=\sqrt{1+t
4
}\) and \(y'(t)=t
2
\) for \(0\le t\le 1\). Which integral gives the arc length over that interval?
A
\(\int_{0}
1
\sqrt{1+t
4
}+t
2
\,dt\)
B
\(\int_{0}
1
\sqrt{(\sqrt{1+t
4
})
2
+(t
2
)
2
}\,dt\)
C
\(\int_{0}
1
\sqrt{1+t
4
+t
2
}\,dt\)
D
\(\int_{0}
1
1+2t
4
\,dt\)
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