AP EAMCET · Maths · Definite Integration
If \(\int_3^b \frac{x-1}{2 x-x^2} d x=\frac{1}{2}\), then \((b-1)^2=\)
- A \(2\)
- B \(\sqrt{2}\)
- C \(1+\frac{3}{\mathrm{e}}\)
- D \(\sqrt{\frac{3}{\mathrm{e}}-1}\)
Answer & Solution
Correct Answer
(C) \(1+\frac{3}{\mathrm{e}}\)
Step-by-step Solution
Detailed explanation
Given \(\int_3^b \frac{x-1}{2 x-x^2} d x=\frac{1}{2} \Rightarrow-\frac{1}{2} \int_3^b \frac{-2 x+2}{2 x-x^2} d x=\frac{1}{2}\)…
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