Prove directly that Eqs. (2) and (3) are equivalent in the following situation. Let be a

Prove directly that Eqs. (2) and (3) are equivalent in the following situation. Let ƒ be a positive decreasing function on [0, b] such that ƒ(b) = 0. Set d = ƒ(0) and g(y) = ƒ ⁻¹(y). Show that

First apply the substitution y = ƒ(x) to the integral on the left and observe that dx = g'(y) dy. Then apply Integration by Parts.

Transcribed Image Text:

= p [². y(length of horizontal cut) dy C M₂ = p = p p["y (81(y) - 82(y)) dy