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  • Find the area of the region bounded by the curve y^2 = x and the lines x = 1, x = 4 and the x-axis in the first quadrant.

Q : 1         Find the area of the region bounded by the curve y^2=x and the lines  x=1,x=4 and the  x-axis in the first quadrant. 

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Area of the region bounded by the curve y^2=x and the lines  x=1,x=4 and the  x-axis in the first quadrant

Area  = \int_{1}^{4}ydy = \int_{1}^{4}\sqrt{x}dx

\left [\frac{x^{\frac{3}{2}}}{\frac{3}{2}} \right ]^4_1 = \frac{2}{3}\left [ (4)^\frac{3}{2}- (1)^\frac{3}{2} \right ]

= \frac{2}{3}\left [ 8 -1 \right ]

= 14/3 units

Posted by

HARSH KANKARIA

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