What is the arc length of f ( x ) = 4 − x 2 on x ∈ [ − 2 , 2 ]?

Question

What is the arc length of   f  (  x  )  =      4    −          x              2             on   x  ∈  [  −  2  ,  2  ]?

Nia Molina · Accepted Answer

d      y              d      x        =            −      x              4      −              x                  2                      (            d      y              d      x            )          2        =            x              2                    4      −              x                  2                    arc length   =  ∫      1    +                  x                  2                            4        −                  x                      2                                d  x  =  2  ∫      1          4      −              x                  2                      d  x  =  arcsin  ⁡  (      x    2    )  +  CFinally, evaluate over [-2,2]arc length   =  2  π

What is the arc length of f ( x ) = 4 − x 2...

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