Mathematics Question on Area between Two Curves

Question

It the area enclosed by the parabolas $P_1: 2 y=5 x^2$ and $P_2: x^2-y+6=0$ is equal to the area enclosed by $P_1$ and $y=\alpha x, \alpha>0$ , then $\alpha^3$ is equal to____

Accepted Answer

The correct answer is 600.
It the area enclosed by the parabolas P1: 2 y=5 x2 and P2: x2-y+6=0

Area =2∫02(x2+6−25x2)dx=0∫52α(αx−25x2)dx
⇒0∫52α(αx−25x2)dx=16
⇒α3=600