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If the area of the region bounded by the curves, y = x², y = 1/x and the lines y = 0 and x = t (t > 1) is 1 sq. unit, then t is equal to -
- 4/3
- e^(2/3)
- 3/2
- e^(3/2)
Correct answer: e^(2/3)
Solution
The area between the curves can be found by integrating the difference of the functions over the specified interval. By setting up the integral and solving for t when the area equals 1 square unit, we find that t must equal e^(2/3) to satisfy this condition.
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