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Definite Integration — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integration2 Marks
MCQ
The value of $\int_3^5 \frac{x^2}{x^2-4} d x$ is
  • A
    $2-\log _e\left(\frac{15}{7}\right)$
  • ✓
    $2+\log _e\left(\frac{15}{7}\right)$
  • C
    $2+4 \log _e 3-4 \log _e 7+4 \log _e 5$
  • D
    $2-\tan ^{-1}\left(\frac{15}{7}\right)$
✓

Answer

Correct option: B.
$2+\log _e\left(\frac{15}{7}\right)$
(B)
$\int_3^5 \frac{x^2}{x^2-4} d x=\int_3^5\left(1+\frac{4}{x^2-4}\right) d x$
$\begin{array}{l}=\left[x+\frac{4}{2(2)} \log \left|\frac{x-2}{x+2}\right|\right]_3^5 \\ =2+\log _c\left(\frac{15}{7}\right)\end{array}$

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