Comprehension

निर्देश : निम्नलिखित प्रश्नों के लिए नीचे दिए गए कथनों पर विचार करें:

माना \(\rm 2\int\frac{x^2-1}{\sqrt{x^2+1}}dx=U(x) V(x)-3\ln \{U(x)+V(x)\}+c\)

U(x) V(x) किसके बराबर है?

This question was previously asked in
NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. \(\rm\sqrt{x^2+x^4}\)
  2. \(\rm\sqrt{x+x^3}\)
  3. \(\rm \frac{\sqrt{x^2+x^4}}{2}\)
  4. \(\rm 2\sqrt{x^2+x^4}\)

Answer (Detailed Solution Below)

Option 1 : \(\rm\sqrt{x^2+x^4}\)
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Detailed Solution

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व्याख्या:

U(x).V(x) = \(x\sqrt{x^2+1}\)

= \(\sqrt{x^4+x^2}\)

इसलिए, विकल्प (a) सही है

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