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Question

Using the method of integration find the area bounded by the curve

[Hint: the required region is bounded by lines x + y = 1, xy = 1, – x + y = 1 and – xy = 11]

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Solution

The area bounded by the curve, , is represented by the shaded region ADCB as

The curve intersects the axes at points A (0, 1), B (1, 0), C (0, –1), and D (–1, 0).

It can be observed that the given curve is symmetrical about x-axis and y-axis.

∴ Area ADCB = 4 × Area OBAO


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