JEE Mains · Maths · STD 12 - 7.2 definite integral
The value of \(b>3\) for which \(12 \int \limits_{3}^{b} \frac{1}{\left(x^{2}-1\right)\left(x^{2}-4\right)} d x=\log _{e}\left(\frac{49}{40}\right)\), is equal to
- A \(6\)
- B \(3\)
- C \(5\)
- D \(9\)
Answer & Solution
Correct Answer
(A) \(6\)
Step-by-step Solution
Detailed explanation
\(\frac{12}{3}\left[\int \limits_{3}^{b}\left(\frac{1}{x^{2}-4}-\frac{1}{x^{2}-1}\right) d x\right]=\log \frac{49}{40}\) \(\frac{12}{3} \cdot\left[\frac{1}{4} \ln \left|\frac{x-2}{x+2}\right|-\frac{1}{2} \ln \left|\frac{x-1}{x+1}\right|\right]_{3}^{b}=\log \frac{49}{40}\)…
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