Consider the polynomials and defined on the interval

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

Problem

Consider the polynomials p(x)=x3−3x2+2p(x)=x^{3}-3x^{2}+2 and q(x)=2x2−4x+1q(x)=2x^{2}-4x+1 defined on the interval [0,3][0,3]. (a) Find the average value of pp on [0,3][0,3]. (b) Find the average value of qq on [0,3][0,3]. (c) State which function has the larger average value on this interval. (d) Calculate, correct to the nearest integer, the percentage by which the larger average value exceeds the smaller one.

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