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  • Find the area of the region bounded by the curve y^2 = 4x and the line x = 3.

Q : 11     Find the area of the region bounded by the curve \small y^2=4x  and the line \small x=3.
 

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The combined figure of the curve y^2=4x and x=3

The required are is OABCO, and it is symmetrical about the horizontal axis.
Therefore, Area of OABCO = 2\times Area of OAB
                                             \\=2[\int_{0}^{3}ydx]\\ =2\int^3_02\sqrt{x}dx\\ =4[\frac{x^{3/2}}{3/2}]^3_0\\ =8\sqrt{3}
therefore the required area is 8\sqrt{3} units.

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manish

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