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NDA 2024 Maths · Mathematics · Definite Integrals · medium

The value of ∫0^1xe^x dx is

Single correct option

The value of ∫01xex dx\displaystyle\int_0^1xe^x\,dx is
  1. A. e−1e-1
  2. B. ee
  3. C. 00
  4. D. 11
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Answer: (D) 11

Integrate by parts: ∫xexdx=xex−ex=(x−1)ex\int xe^xdx=xe^x-e^x=(x-1)e^x. Then [(x−1)ex]01=0−(−1)=1\left[(x-1)e^x\right]_0^1=0-(-1)=1. Trap: e−1e-1 is ∫01exdx\int_0^1e^xdx, and forgetting the lower-limit contribution −(−1)-(-1) gives 0.
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Original question written in the NDA 2024 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake