3.Find the area of the region bounded by the curve y= x, the x axis and the lines x=1 and x=e. (10%)

8. Let the probabilities for characters A, B, C, D, E, F to appear in acharacter string be \( \frac{5}{54} \), \( \frac{6}{54} \), \( \frac{7}{54} \), \( \frac{9}{54} \), \( \frac{10}{54} \), and \( \frac{17}{54} \)respectively. Findbinary codes for these characters such that when a characterstring of these characters is represented by your code the binarystring will be of minimal length. Is 010101010101010 a binarystring corresponding to a character string in your code? Describehow do you find the character string of a binary string in yourcode? [10%]

3.Find the area of the region bounded by the curve \( y=\ln x \), the \( x \) axis and the lines \( x=1 \) and \( x=e \). (10%)

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