Find the arc length from (0,3) clockwise to `(2,sqrt(5))` along the circle `x^2+y^2 = 9`

Expert Answers

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Use the arc length formula,


`ds=sqrt(1+(dy/dx)^2)dx` , if y=f(x), a`<=` x`<=` b

GivenĀ `x^2+y^2=9`





Plug in the above in ds,





The limits are x=0 and x=2,

`L=int_0^2 3/sqrt(9-x^2)dx`

`=3int_0^2 1/sqrt(9-x^2)dx`

Now let's first evaluate the indefinite integral by using integral substitution,

LetĀ `x=3sin(u)`








substitute back u and add a constant C to the solution,






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