question a b Let f: [a, b] → R be a continuous and strictly increasing function which maps the interval [a, b]f(b). Denote by g: [c, d] → R theinverse function of f. Notice that f [a, b] → R and g: [c, d] → R are Riemann integrable.bijectively onto the interval [c, d], where c = f(a), and d=:This question is regarding the proof of the formulabrdS. f(x)dx = bf(b) — aƒ(a) – ["²9-(a) If a > 0 and c> 0, draw a figure to illustrate the formula (**).g(x)dx.(b) If f is continuously differentiable on (a, b), use integration by substitution with u = g(x)to prove the formula (**).(i) Show thati=0(c) Let Pn = {x}o be the regular partition of the interval [a, b] into n intervals. For 0 ≤ isn, let y; = f(x;). Then Pn = {y}?o is a partition of [c, d].n(**)nΣ ƒ (Xi-1) (Xi − Xi−1) + Σ9(Yi) (Yi − Yi−1) = bf (b) — af (a).i=1i=1(ii) Show that lim |P| = 0 and lim |P|n4xnxity.(iii) Use part (i) and part (ii) to prove the formula (**).=0. You might want to use uniform continu-

Given that is a continuous and strictly increasing function which maps the interval [a,b]…

This question is regarding the proof of the formula rd [*° f(x)dx = bƒ(b) — aƒ(a) – [ª g(x - g(x)dx. (a) If a > 0 and c> 0, draw a figure to illustrate the formula (**). (**) (b) If f is continuously differentiable on (a, b), use integration by substitution with u = g(x) to prove the formula (**).