GATE 2019 ME (ME1) – Question 61
Evaluate $\int_1^e x\ln x\,dx$, to three decimal places.
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Show answer and explanation
Correct answer: 2.090 to 2.104
Explanation
Integrate by parts with u=ln x and dv=x dx. An antiderivative is $(x^2/2)\ln x-x^2/4$. Evaluation at e and1 gives $(e^2+1)/4=2.097264$,rounded **2.097**. The lower-limit term is negative and must be subtracted.