Area Under the Curve
Area Under a Curve
Premium Question
Grade 12
Question:
The area bounded by the curve $y = e^{-x}$, the coordinate axes, and the line $x = 1$ is:
(1) $\frac{e - 1}{e}$
(2) $\frac{e + 1}{e}$
(3) $1 - e$
(4) $\frac{1}{e}$
Step-by-Step Solution
Key Concept: Recognise the (geometric) area as $\int_0^1 e^{-x} \, dx$ and find its antiderivative directly.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)