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1

Find the area of the region in the first quadrant bounded by the parabola y = 4x^{2} and the lines x = 0, y = 1 and y = 4.

To find the area under two or more than two curves, the first crucial step is to find the INTERSECTION POINTS of the curves.

The coordinates

⟹ y = 4x^{2}, y = 4

⟹ 4 = 4x^{2}

⟹ x = + 1

Required Area can be calculated by breaking the problem into two parts.

I. Calculate Area under the curve A and Line C

II. Subtract the area enclosed by curve A and Line B from the above area.

Therefore, the areas are:

I. = Area enclosed by line C and curve A

II. = Area enclosed by curve A and Line B.

Now the required area under the curves: