Assume that is smooth on [a, b] and partition the interval [a, b] in the usual

Assume that ƒ is smooth on [a, b] and partition the interval [a, b] in the usual way. In each subinterval [x_k-1, x_k], construct the tangent fin at the point (x_k-1, ƒ(x_k-1)), as shown in the accompanying figure.

a. Show that the length of the kth tangent fin over the interval [x_k-1, x_k] equals

b. Show that

which is the length L of the curve y = ƒ(x) from a to b.

Transcribed Image Text:

V(1x)2 + (f′(xx-1) Δx).