Question

Find the area bounded by the curves x = y² and x = 3 – 2y².

Answer 1

To find area bounded by

X = y² …(i)

And X = 3 – 2y² …(ii)

On solving the equation (i) and (ii),

y² = 3 – 2y²

Or 3y² = 3

Or y = \(\pm\)1

When y = 1 then x = 1 and when y = – 1 then x = 1

Equation (i) represents an upward parabola with vertex (0, 0) and axis – y.

Equation (ii) represents a parabola with vertex (3, 0) and axis as x – axis.

They intersect at A (1, – 1) and C (1, 1)

These are shown in the graph below: -

Required area = Region OABCO

= 2 Region OBCO

= 2[Region ODCO + Region BDCB]

The area bounded by the curves x = y² and x = 3 – 2y² is 4 sq. units.