Question

The area of the curve xy² =  4(2 – x) bounded by Y-axis is ______.

Options

• 4π

• 8π

• 12π

• 16π

Answer 1

The area of the curve xy² =  4(2 – x) bounded by Y-axis is 4π.

Explanation:

Since the curve is symmetrical about X-axis.

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

Put x = `2sin^2theta`

⇒ dx = `4 sin theta . cos theta  "d"  theta`

∴ A = `4 int_0^(pi/2) sqrt((2cos^2theta)/(2sin^2theta)) . 4 sintheta cos theta  "d"theta`

= `16 int_0^(pi/2) costheta/sin theta sin theta cos theta  "d" theta`

= `16 int_0^(pi/2) cos^2theta  "d"theta`

= `16 . 1/2. pi/2` = 4π