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JEE Mains · Maths · STD 12 - 7.1 indefinite integral
If \(f\,(x)\, = \,\int {\frac{{5{x^8}\, + \,7{x^6}}}{{{{({x^2} + 1 + 2{x^7})}^2}}}dx\,,(x\, \ge \,0\,)} \) and \(f\,(0)\,=\,0,\) then the value of \(f (1)\) is
- A \(-\frac {1}{2}\)
- B \(\frac {1}{2}\)
- C \(-\frac {1}{4}\)
- D \(\frac {1}{4}\)
Answer & Solution
Correct Answer
(D) \(\frac {1}{4}\)
Step-by-step Solution
Detailed explanation
\(\int {\frac{{5{x^8} + 7{x^6}}}{{{{\left( {{x^2} + 1 + 2{x^7}} \right)}^2}}}} dx\) \( = \int {\frac{{5{x^{ - 6}} + 7{x^{ - 8}}}}{{{{\left( {\frac{1}{{{x^7}}} + \frac{1}{{{x^5}}} + 2} \right)}^2}}}} dx\) \( = \frac{1}{{2 + \frac{1}{{{x^5}}} + \frac{1}{{{x^7}}}}} + C\)…
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