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  • Find the area of the region lying in the first quadrant and bounded by y = 4x^2, x = 0, y = 1 and y = 4.

Q : 3  Find the area of the region lying in the first quadrant and bounded by  \small y=4x^2,x=0,y=1 and  \small y=4.

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the area of the region lying in the first quadrant and bounded by  \small y=4x^2,x=0,y=1 and \small y=4.


The required area (ABCD) = 
                                          \\=\int_{1}^{4}xdy\\ =\int_{1}^{4}\frac{\sqrt{y}}{2}dy\\ =\frac{1}{2}.\frac{2}{3}[y^{3/2}]_1^4\\ =\frac{1}{3}[8-1]\\ =\frac{7}{3}
The area of the shaded region is 7/3 units

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manish

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