∫ 0 2 x e x d x =, e 2 + 1, e 2 − 1, e − 1 − 1, e − 1 + 1

∫ 0 2 x e x d x = x ∫ e x d x - ∫ d x d x ∫ e x d x d x 0 2 = x e x - e x 0 2 = 2 e 2 - e 2 - 0 × e 0 - e 0 = e 2 + 1

∫ 0 2 x e x d x =

Question: Answered & Verified by Expert

\int_{0}^{2} x e^{x} d x =

MathematicsDefinite IntegrationAP EAMCETAP EAMCET 2021 (19 Aug Shift 2)

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Solution:

2132 Upvotes Verified Answer

The correct answer is:

e^{2} + 1

$\int_{0}^{2} x e^{x} d x = {[x \int e^{x} d x - \int (\frac{d x}{d x} \int e^{x} d x) d x]}_{0}^{2}$

$= {[x e^{x} - e^{x}]}_{0}^{2} = (2 e^{2} - e^{2}) - (0 \times e^{0} - e^{0}) = e^{2} + 1$

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