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Wind Turbine Energy from Power Integral

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The power output of a wind turbine, in kilowatts (kW), is described by the function P(t)=200(1−e−0.1t)P(t) = 200(1 - e^{-0.1t}), where tt is the time in hours. The total energy EE, in kilowatt-hours (kWh), produced by the turbine from t=0t=0 to t=10t=10 hours is given by the integral E=∫010200(1−e−0.1t) dtE = \int_{0}^{10} 200(1 - e^{-0.1t}) \,dt. Which of the following best approximates the total energy produced?

A

Approximately 920 kWh920 \text{ kWh}

B

Approximately 2000∗e−1≈736 kWh2000*e^{-1} \approx 736 \text{ kWh}

C

Approximately 800 kWh800 \text{ kWh}

D

Approximately 600 kWh600 \text{ kWh}

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