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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.

Q : 2         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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Area of the region bounded by the curve y^2=9x,x=2,x=4 and the  x-axis in the first quadrant

Area  = \int_{2}^{4}ydy = \int_{2}^{4}\sqrt{9x}dx = 3\int_{2}^{4}\sqrt{x}dx

3\left [\frac{x^{\frac{3}{2}}}{\frac{3}{2}} \right ]^4_2 = 3.\frac{2}{3}\left [ (4)^\frac{3}{2}- (2)^\frac{3}{2} \right ]

= 2\left [ 8 -2\sqrt2 \right ]

= \left [ 16 -4\sqrt2 \right ] units

Posted by

HARSH KANKARIA

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