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Mathematics - Area under the curve Question with Solution | TestHub

MathematicsArea under the curveArea under the curveMedium2 minPYQ_2025

MathematicsMediumsingle choice

The area of the region enclosed by the curves $y = e^{x}, y = ∣ e^{x} - 1 ∣$ and $y$ -axis is:

Question diagram: The area of the region enclosed by the curves y = e x , y =

Options:

Answer:

Solution:

$e^{x} = 1 - e^{x} \Rightarrow 2 e^{x} = 1 \Rightarrow e^{x} = \frac{1}{2} \Rightarrow x = ln \frac{1}{2} \int_{l n (1/2)}^{0} [e^{x} - (1 - e^{x})] d x = \int_{l n 2}^{0} (2 e^{x} - 1) d x = 2 e^{x} - x ∣_{- l n 2}^{0} = 2 - (1 + ln 2) = 1 - lo g_{e} 2$

Stream:JEESubject:MathematicsTopic:Area under the curveSubtopic:Area under the curve

⏱ 2mℹ️ Source: PYQ_2025

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