1. Let f: [a, b] → R be a strictly increasing function, which is continuous on [a, b] and differentiable on (a, b). (a) Show that X f(x) -1 Så ƒ(t) dt + [{²ð ƒ¯¹(1) dl = rf(x) — aƒ(a), ¥x€([a,b]. a f(a) Give a geometric interpretation of this equality. 2 2 (b) Compute √ √t dt and f² ln(t) dt using the result obtained in the previous part.

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