Q199 / 270 · NDA 2013 (Phase 2) · Mathematics

What is $\int_0^2 e^{\ln x} d x$ equal to?

  • A
    1
  • Correct answer
    B
    2
  • C
    4
  • D
    None of the above

Solution

$\mathrm{I}=\int_0^2 e^{\ln x} \cdot d x$ Let $e^{\ln (x)}=y$ or, $\ln (x)=\ln (y)$ $\begin{aligned} & x=y \Rightarrow d x=d y \\ & \mathrm{I}=\int_0^2 y \cdot d y=\left[\frac{y^2}{2}\right]_0^2=2-0=2 \end{aligned}$

Hence, the correct answer is option: 'B'.

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