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The area of the region R = {(x,y): xy ≤ 8, 1 ≤ y ≤ x², x ≥ 0} is
- 1/3 (49 logₑ(2) − 15)
- 2/3 (20 logₑ(2) + 9)
- 2/3 (24 logₑ(2) − 7)
- 1/3 (40 logₑ(2) + 27)
Correct answer: 2/3 (24 logₑ(2) − 7)
Solution
The correct option is derived from calculating the area bounded by the curves defined by the inequalities, specifically integrating the appropriate functions within the specified limits, which leads to the expression 2/3 (24 logₑ(2) − 7) as the area of region R.
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