TS EAMCET · Maths · Definite Integration
\(\int_2^3 \frac{d x}{x^2-x}\) is equal to
- A \(\log \frac{2}{3}\)
- B \(\log \frac{4}{3}\)
- C \(\log \frac{8}{3}\)
- D \(\log \frac{1}{4}\)
Answer & Solution
Correct Answer
(B) \(\log \frac{4}{3}\)
Step-by-step Solution
Detailed explanation
We have, \[ \begin{aligned} \int_2^3 \frac{d x}{x^2-x} & =\int_2^3 \frac{1}{x(x-1)} d x \\ & =\int_2^3\left[-\frac{1}{x}+\frac{1}{x-1}\right] d x \\ & =\left[\log \frac{x-1}{x}\right]_2^3=\log \frac{2}{3}-\log \frac{1}{2}=\log \frac{4}{3} \end{aligned} \]
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