MHT CET · Maths · Definite Integration
\(\int_0^1 \frac{1}{2+\sqrt{x}} \mathrm{~d} x=\)
- A \(2 \log \left(\frac{2 e}{3}\right)\)
- B \(2 \log \left(\frac{4 e}{9}\right)\)
- C \(\log \left(\frac{2 \mathrm{e}}{3}\right)\)
- D \(\log \left(\frac{4 \mathrm{e}}{9}\right)\)
Answer & Solution
Correct Answer
(B) \(2 \log \left(\frac{4 e}{9}\right)\)
Step-by-step Solution
Detailed explanation
Let \(u=\sqrt{x}\), then \(dx=2u\,du\). Limits: \(x=0 \to u=0\), \(x=1 \to u=1\). \(\int_0^1 \frac{2u}{u+2}\,du = \int_0^1 \left(2-\frac{4}{u+2}\right)\,du\)
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