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Find the area of the region bounded by the line y = x, the vertical line x = e, the curve y = 1/x, and the positive x-axis.
- 1 square unit
- 3/2 square units
- 5/2 square units
- 1/2 square unit
Correct answer: 3/2 square units
Solution
The area is found by integrating the difference between the curves y = 1/x and y = x from x = 1 to x = e, which results in an area of 3/2 square units. This accounts for the region bounded above by y = 1/x and below by y = x, along with the vertical line at x = e.
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