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Dear student,

C_{1} \Rightarrow y = x^{2} C_{2} \Rightarrow y = 2 x l e t p o i n t P (a, a^{2}) u \sin g C_{1} a n d C_{2} Q (\frac{a^{2}}{2}, a^{2}), R (a, f (a)) a r e a O P Q = \int_{0}^{a^{2}} (\sqrt{y} - \frac{y}{2}) d y = {[\frac{2}{3} y^{\frac{3}{2}} - \frac{y^{2}}{4}]}_{0}^{a^{2}} = [\frac{2}{3} a^{3} - \frac{a^{4}}{4}] a r e a O R P = \int_{0}^{a} (x^{2} - f (x)) d x = a r e a O P Q [\frac{2}{3} a^{3} - \frac{a^{4}}{4}] = \int_{0}^{a} (x^{2} - f (x)) d x d i f f e r e n t i a t e w . r . t a 2 a^{2} - a^{3} = a^{2} - f (a) + C f (a) = a^{3} - a^{2} + C f (0) = 0, C = 0 t h e n f (x) = x^{3} - x^{2} a n s w e r

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