Question

The area of the region bounded by the curve y = `sqrt(16 - x^2)` and x-axis is ______.

Options

• 8 sq.units

• 20π sq.units

• 16π sq.units

• 256π sq.units

Answer 1

The area of the region bounded by the curve y = `sqrt(16 - x^2)` and x-axis is 8 sq.units.

Explanation:

Here, equation of curve is y = `sqrt(16 - x^2)`

Required area = `2[int_0^4 sqrt(16 - x^2)  "d"x]`

= `2[x/2 sqrt(16 - x^2) + 16/2 sin^-1  x/4]_0^4`

= `2[(0 + 8 sin^-1 4/4) - (0 + 0)]`

= `2[8sin^-1 (1)]`

= `16 * pi/2`

= 8 sq.units.