Answer :

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 = 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 – 2 y2 is


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