Question:

For 1x1-1\le x\le1, if f (x) is the sum of the convergent power series x+x222+x332+...+xnn2+...x+\frac{x^2}{2^2}+\frac{x^3}{3^2}+...+\frac{x^n}{n^2}+... then f(12)f(\frac{1}{2}) is equal to

Updated On: Oct 1, 2024
  • 012In(1t)tdt.\displaystyle\int\limits^{\frac{1}{2}}_{0}\frac{In(1-t)}{t}dt.
  • 012In(1t)tdt.-\displaystyle\int\limits^{\frac{1}{2}}_{0}\frac{In(1-t)}{t}dt.
  • 012tIn(1+t)dt.\displaystyle\int\limits^{\frac{1}{2}}_{0}tIn(1+t)dt.
  • 012tIn(1t)dt.\displaystyle\int\limits^{\frac{1}{2}}_{0}tIn(1-t)dt.
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The Correct Option is B

Solution and Explanation

The correct option is (B): 012In(1t)tdt.-\displaystyle\int\limits^{\frac{1}{2}}_{0}\frac{In(1-t)}{t}dt.
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