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प्रश्न
Find the area bounded by the curve y = |x – 1| and y = 1, using integration.
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उत्तर
We have, y = (x – 1)
y = x – 1, if x – 1 ≥ 0
y = –x + 1, if x – 1 < 0
Required Area = Area of shaded region
A = `int_0^2 ydx`
= `int_0^1(1 - x)dx + int_1^2(x - 1)dx`
= `[x - x^2/2]_0^1 + [x^2/2 - x]_1^2`
= `(1 - 1/2) - (0 - 0/2) + (4/2 - 2) - (1/2 - 1)`
= `1/2 + 1/2`
= 1 sq.unit
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