If f(x)=\lim_{n \to \infty} n^2 (x^{\frac{1}{n}}-x^{\frac{1}{n+1}}) , x>0, then \int x f(x) \dx=

Correct Answer is : x22logx−x24+C

\frac{x^2}{2} \log x+\frac{x^2}{4}+C

\frac{x^2}{2} \log x-\frac{x^2}{4}+C

-\frac{x^2}{2} \log x+\frac{x^2}{4}+C

AP EAPCET 17th May 2023 Shift 2 Solved Paper

Section: Mathematics

Question : 70 of 160

Marks: +1, -0

If f(x)=

lim

n→∞

n2(x‌

−x‌

n+1

),x>0, then ∫xf(x)‌dx=

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