Without evaluating the integral

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

Problem

Without evaluating the integral, explain in one or two sentences why there must exist at least one c∈(0,2)c\in(0,2) satisfying ∫02ex dx=ec (2−0).\int_{0}^{2} e^{x}\,dx = e^{c}\,(2-0).

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