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Definite Integration — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integration2 Marks
MCQ
$\int_1^3\left(\frac{x^2+1}{4 x}\right)^{-1} d x=$
  • A
    $\log 5$
  • B
    $\frac{1}{2} \log 5$
  • ✓
    $\log 25$
  • D
    $\log 100$
✓

Answer

Correct option: C.
$\log 25$
(C)
$\int_1^3\left(\frac{x^2+1}{4 x}\right)^{-1} d x$
$\begin{array}{l}=2 \int_1^3 \frac{2 x}{1+x^2} d x \\ =2\left[\log \left(1+x^2\right)\right]_1^3 \\ =2(\log 10-\log 2) \\ =\log \left(\frac{10}{2}\right)^2 \\ =\log 25\end{array}$

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