Project ForgeEngineering Mathematics
Calculus
GATE 2019
Medium
The value of the definite integral ∫₁ᵉ (x ln x) dx is (round off to three decimal places)
2.097(± 0.007 accepted)
Explanation
By parts with u=ln x, dv=x dx: ∫x ln x dx = (x²/2)ln x − x²/4. Evaluating from 1 to e: [e²/2·1 − e²/4] − [0 − 1/4] = e²/4 + 1/4 = (e²+1)/4 ≈ (7.389+1)/4 ≈ 2.097.
Source: GATE ME 2019 Session 1 (Set 1) (2019)
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