Question

The area of the region bounded by the circle x² + y² = 1 is ______.

पर्याय

• 2π sq.units

• π sq.units

• 3π sq.units

• 4π sq.units

Answer 1

The area of the region bounded by the circle x² + y² = 1 is π sq.units.

Explanation:

Given equation of circle is x² + y² = 1

⇒ y = `sqrt(1 - x^2)`

Since the circle is symmetrical about the axes.

∴ Required area = `4 xx int_0^1 sqrt(1 - x^2)  "d"x`

= `4[x/2 sqrt(1 - x^2) + 1/2 sin^-1 x]_0^1`

= `4[0 + 1/2 sin^-1 (1) - 0 - 0]`

= `4 xx 1/2 xx pi/2`

= π sq.units