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Find the arc length of the curve on the given interval. (Round your answer to three decimal places.) Parametric Equations Interval x=√t​, y=2t−70≤t≤1 .

1 Answer

6 votes

Answer:

2.323

Explanation:

Recall the parametric arc length formula
\displaystyle L=\int^b_a\sqrt{\biggr((dx)/(dt)\biggr)^2+\biggr((dy)/(dt)\biggr)^2}\,dt


\displaystyle x=√(t)\rightarrow(dx)/(dt)=(1)/(2√(t))\\\\y=2t-7\rightarrow(dy)/(dt)=2


[a,b]=[0,1]


\displaystyle L=\int^1_0\sqrt{\biggr((1)/(2√(t))\biggr)^2+2^2}\,dt\\\\L=\int^1_0\sqrt{(1)/(4t)+4}\,dt\approx2.323

User Mohan Raj B
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