# How do you find the arc length of the curve y = sqrt( 2 − x^2 ), 0 ≤ x ≤ 1?

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I want someone to double check my answer

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Gió Share
Jul 30, 2015

I found: $s = \sqrt{2} \frac{\pi}{4} = 1.11$

#### Explanation:

I plotted the arc you need (a bit of a cirle) and found:

The arc length $s$ is given as:
$s = r \cdot \theta$
where $r = \sqrt{2}$ is the radius (obtained setting $x = 0$ into the function) and theta=45°=pi/4 is the angle (we need to use radians). So you get that:
$s = \sqrt{2} \frac{\pi}{4} = 1.11$

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