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प्रश्न
Find the area of the region bounded by the parabola y2 = 4x and the line x = 3.
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उत्तर
Given equation of the parabola is y2 = 4x
∴ `y = 2sqrt(x)` ...[∵ In first quadrant, y > 0]
And equation of the line is x = 3
∴ Required = Area of the region OQRPO
= 2(Area of the region ORPO)
= `2 int_0^3y.dx`
= `2 int_0^3 2sqrt(x).dx`
= `4 int_0^3 sqrt(x).dx`
= `4 int_0^3 x^(1/2).dx`
= `4[(x^(3/2))/(3/2)]_0^3`
= `4 xx (2)/(3)[(3)^(3/2) - 0]`
= `8/3(3sqrt(3))`
∴ Required area = `8sqrt(3)` sq. units.
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