Question

Find the area of the region in the first quadrant bounded by the parabola y = 4x² and the lines x = 0, y = 1 and y = 4.

Answer 1

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

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. \(\int^1_0 (4 - 4x^2).dx\) = Area enclosed by line C and curve A

II. \(\int^\frac{1}{2}_0 (1 - 4x^2).dx\) = Area enclosed by curve A and Line B.

Now the required area under the curves:

Area bounded = \(\frac{7}{3}\) square units.