Question

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 .

Answer 1

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`