Find the area of the region bounded by the graphs of ,y = 0,x = 0,and x = 1.

Name: Find the area of the region bounded by the graphs of ,y = 0,x = 0,and x = 1.
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Question

Find the area of the region bounded by the graphs of  ,y = 0,x = 0,and x = 1. ​

Quizplus · Accepted Answer

The region is bounded by the curve $y=e^{-x}$, the x-axis, and the lines $x=0$ and $x=1$. To find the area, we integrate $e^{-x}$ with respect to $x$ from $0$ to $1$:
$$\int_0^1 e^{-x}dx = -e^{-x}\bigg|_0^1 = -e^{-1} + e^{0} = 1-e^{-1} \approx 0.632$$
Therefore, the area is approximately $0.632$, which is closest to choice letter A.

Find the Area of the Region Bounded by the Graphs