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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: $\int_0^1 \frac{1}{\sqrt{1+x^2}} d x$ is:
  • A
    $\log \sqrt{2}$
  • ✓
    $\log (1+\sqrt{2})$
  • C
    $\log (1-\sqrt{2})$
  • D
    $\frac{1}{\log (1+\sqrt{2})}$
✓

Answer

Correct option: B.
$\log (1+\sqrt{2})$
(B) $\log (1+\sqrt{2})$
$\int_0^1 \frac{1}{\sqrt{1+x^2}} d x=\log \left|x+\sqrt{1+x^2}\right|_0^1$
$=\log \left|1+\sqrt{1+1^2}\right|-\log |0+\sqrt{1+0}|$
$=\log (1+\sqrt{2})-\log 1$
$=\log (1+\sqrt{2}) \quad[\because \log 1=0]$

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