If f(x) = 2 (e^x/2) , what is the area bounded by f(x) for the interval [0, 2] on the x-axis? - Mathematics MCQ Mathematics Mock Test - 3 2026 | ExamTest.live

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If f (x) = 2 ln (e^{x /2}), what is the area bounded by f (x) for the interval [0, 2] on the x-axis?

Solution & Step-by-step Explanation

Simplify f (x) : f (x) = 2 \cdot \frac{x}{2} ln (e) = x The area bounded by y = x from x = 0 to x = 2 is: Area = \int_{0}^{2} x d x = [\frac{x ^{2}}{2}]_{0}^{2} = \frac{4}{2} - 0 = 2

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If f (x) = 2 ln (e^{x /2}), what is the area bounded by f (x) for the interval [0, 2] on the x-axis?

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