Let the average value of a continuous function on be

MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Let the average value of a continuous function ff on [a,b][a,b] be MM. For constants A,B(>0),C,DA,B(>0),C,D, consider g(x)=Af(Bx+C)+Dg(x)=A f(Bx + C)+D on the interval [a−CB, b−CB]\bigl[\dfrac{a-C}{B},\,\dfrac{b-C}{B}\bigr]. Express the average value of gg on this interval in terms of A,D,A, D, and MM.

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