Question

Find the area of the region bounded by the parabola:

y = 4 – x² and the X-axis.

Answer 1

The equation of the parabola is y = 4 – x²

∴ x² = 4 – y

i.e. (x – 0)² = -(y – 4)

It has vertex at P(0, 4)

For points of intersection of the parabola with X-axis,

we put y = 0 in its equation.

∴ 0 = 4 – x²

∴ x² = 4

∴ x = ± 2

∴ the parabola intersect the X-axis at A(-2, 0) and B(2, 0)

Required area = area of the region APBOA 

= 2[area of the region OPBO]