Let be a continuous function on

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let ff be a continuous function on [a,b][a, b]. Prove that there exists a number x∈[a,b]x \in [a, b] such that ∫axf(t)dt=∫xbf(t)dt\int_{a}^{x} f(t) dt = \int_{x}^{b} f(t) dt .

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