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प्रश्न
Find the area bounded by the curve y = sin x between x = 0 and x = 2π.
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उत्तर
Some points on the graph of y = sin x are as follows. The graph is obtained by joining these points with a curve.
| x | 0 | `pi/6` | `pi/4` | `pi/3` | `pi/2` | `(5pi)/6` | `(3pi)/4` | `(2pi)/3` | `pi` |
| y | 0 | 0.5 | 0.7 | 0.8 | 1 | 0.5 | 0.7 | 0.8 | 0 |
Area of the required region
= Area of the region bounded by the curve OPAQB and the x-axis
= Area of sector OPA + Area of sector AOB
= 2 Area of sector OPA
`= 2 int_0^pi sin x dx`
`= 2 [- cos x]_0^pi`
= 2[1 + 1]
= 2 × 2
= 4 square unit
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