# Q : 2         Find the area of the region bounded by  $\dpi{100} y^2=9x,x=2,x=4$  and the $\dpi{100} x$-axis in the first quadrant.

H Harsh Kankaria

Area of the region bounded by the curve $\dpi{100} y^2=9x,x=2,x=4$ and the  $\dpi{100} x$-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

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