Let be an increasing function on [a, b] and let g be its inverse. Argue on

Let ƒ be an increasing function on [a, b] and let g be its inverse. Argue on the basis of arc length that the following equality holds:

Then use the substitution u = ƒ(x) to prove Eq. (4).

Transcribed Image Text:

f(b) S* √₁ = [² 1 + f'(x)² dx a f(a) 1 + g' (y)² dy