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Find the area of the region bounded by `y^2=9x ,``x = 2, x = 4`and the x-axis in the first quadrant.

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Given curve `y^(2)=9x` is a parabola which is symmetric to X-axis.

The area of the region bounded by the curve `y^(2)=9x, x=2` and `x=4` and X-axis is shown in the figure.
` :. ` Required area
`=int_(2)^(4)|y|dx=int_(2)^(4)3sqrt(x)dx`
`=3[(x^(3//2))/((3)/(2))]_(2)^(4)=(3xx2)/(3)(4^(3//2)-2^(3//2))`
`=2(4sqrt(4)-2sqrt(2))=2(8-2sqrt(2))`
`=4(4-sqrt(2))` sq. units.
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