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Integrals and it's Applications — Applied Maths STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceApplied MathsIntegrals and it's Applications1 Mark
MCQ
The value of $\int\left[\sqrt{x}+\frac{1}{\sqrt{x}}\right]^2 d x$ is
  • A
    $x^2-2 x+\log |x|+C$
  • ✓
    $\frac{x^2}{2}+2 x+\log |x|+C$
  • C
    $x^2+2 x-\log |x|+C$
  • D
    $x^2-x+\log |x|+C$
✓

Answer

Correct option: B.
$\frac{x^2}{2}+2 x+\log |x|+C$
(B) $\frac{x^2}{2}+2 x+\log |x|+C$
$\begin{aligned} I & =\int\left[\sqrt{x}+\frac{1}{\sqrt{x}}\right]^2 d x \\ & =\int\left(x+\frac{1}{x}+2\right) d x \\ & =\int x d x+\int \frac{1}{x} d x+2 \int d x \\ & =\frac{x^2}{2}+\log |x|+2 x+C\end{aligned}$

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