Area between two curves f and g is given by:
A = ∫ab(f(y)−g(y))dy where a<y<b
Here,
g = y2=ax
x=ay2
f = ay2=x3
x=a1/3y2/3
A = ∫−aa(−ay2+a1/3y2/3)dy
=∫−aa−ay2dy+∫−aaa1/3y2/3dy
=3a−y3∣∣−aa+53y5/3a1/3∣∣−aa
=−3a2+53a2−3a2+53a2
= −32a2+56a2
= 15−10a2+18a2
=158a2
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