State which of the following expressions equals the average value of a continuous…

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

State which of the following expressions equals the average value of a continuous function ff on the closed interval [a,b][a,b] (a<ba<b). (a) ∫abf(x) dx\displaystyle\int_a^b f(x)\,dx (b) 1b−a∫abf(x) dx\dfrac{1}{b-a}\displaystyle\int_a^b f(x)\,dx (c) 1b∫abf(x) dx\dfrac{1}{b}\displaystyle\int_a^b f(x)\,dx (d) 1b−a∫0bf(x) dx\dfrac{1}{b-a}\displaystyle\int_0^{b} f(x)\,dx

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