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

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Gió Share
Jul 30, 2015

Answer:

I found: #s=sqrt(2)pi/4=1.11#

Explanation:

I plotted the arc you need (a bit of a cirle) and found:
enter image source here
The arc length #s# is given as:
#s=r*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)pi/4=1.11#

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