What is the area under the curve f(x) = xe^x above the x-axis and between x = 0 and x = 1 ? - Mathematics MCQ Mathematics Mock Test - 3 2026 | ExamTest.live

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1 mark

What is the area under the curve f (x) = x e^{x} above the x-axis and between x = 0 and x = 1 ?

Solution & Step-by-step Explanation

Area = \int_{0}^{1} x e^{x} d x Use integration by parts: \int u d v = uv - \int v d u u = x, d v = e^{x} d x ⟹ d u = d x, v = e^{x} $ Area = [x e^{x} - e^{x}]_{0}^{1} $ (1 \cdot e^{1} - e^{1}) - (0 \cdot e^{0} - e^{0}) = (e - e) - (0 - 1) = 0 + 1 = 1

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What is the area under the curve f (x) = x e^{x} above the x-axis and between x = 0 and x = 1 ?

1/2 square unit

1 square unit

3/2 square unit

2 square unit

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