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The area enclosed between the x-axis, the curve y = 1 + 8/x², and the ordinates x = 1 and x = 2 is divided into two equal parts by the ordinate x = a. If a can be written as a = (3 + sqrt(p))/8, find the value of p.

1. 70
2. 71
3. 72
4. 73

Correct answer: 73

Solution

The condition that x = a bisects the area means the integral from 1 to a equals half the total integral from 1 to 2. Solving the resulting quadratic 4a² - 3a - 4 = 0 yields a = (3 + sqrt(73))/8.

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