For in , it is known that . Which of the following correctly compares the two…

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

For xx in [0,1][0,1], it is known that ex≥1+xe^{x}\ge 1+x. Which of the following correctly compares the two integrals ∫01ex dx\displaystyle\int_{0}^{1} e^{x}\,dx and ∫01(1+x) dx\displaystyle\int_{0}^{1} (1+x)\,dx? (a) ∫01ex dx=∫01(1+x) dx\displaystyle\int_{0}^{1} e^{x}\,dx = \int_{0}^{1} (1+x)\,dx (b) ∫01ex dx>∫01(1+x) dx\displaystyle\int_{0}^{1} e^{x}\,dx > \int_{0}^{1} (1+x)\,dx (c) ∫01ex dx<∫01(1+x) dx\displaystyle\int_{0}^{1} e^{x}\,dx < \int_{0}^{1} (1+x)\,dx (d) The relation cannot be determined without evaluating both integrals exactly

Related theory

Browse the problem library