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Find the area of the region enclosed between the curve f(x) = (x² - 1)/(x² + 1) and the line y = 1.
- pi sq. units
- 2*pi sq. units
- pi/2 sq. units
- none of these
Correct answer: 2*pi sq. units
Solution
The vertical gap between y=1 and the curve is 2/(x²+1); integrating this from -infinity to infinity gives 2*[arctan x] = 2*pi.
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