Find the area bounded by the curves x = y^{2} and x = 3 – 2 y^{2}.

To find area bounded by

X = y^{2} …(i)

And

X = 3 – 2y^{2} …(ii)

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

y^{2} = 3 – 2y^{2}

Or 3y^{2} = 3

Or y = 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 = y^{2} and x = 3 – 2 y^{2} is

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