Question

arc length

Answer 1

what's the f(x)?

Answer 2

\[y =\sqrt{2-x ^{2}}\]

Answer 3

so f(x) = sqrt(2-x^2)? i think my computer is not showing me this properly...

Answer 4

yes

Answer 5

ok, so we don't need to use f(x) or f'(x). notice that your equation can be written as:
y^2 = 2 - x^2 or
x^2 + y^2 = 2
which is a ....

Answer 6

square both sides of your equation.... and get both variables to the left side...

Answer 7

what do you do after that do you still have to put the y= into the arc lenght formula

Answer 8

i need to leave so... lemme just finisht this...
x^2 + y^2 = 2 is the equation of a circle centered at (0, 0) with radius sqrt(2).
since your equation is y = sqrt(2-x^2), this is only the top half of that circle.
so to get arclength of y = sqrt(2 - x^2), just take half the circumference of that circle.
Since circumference = 2*pi*(radius) = 2*pi*sqrt(2), half of that is pi*sqrt(2)...
So your arclength is pi*sqrt(2)...