If the area of the region $\left\{ (x,y):1 - 2x \right.\ $ y $4 - x^{2}$, $x \geq 0,y \geq 0\}$ is $

Question

If the area of the region $\left\{ (x,y):1 - 2x \right.\ $ y $4 - x^{2}$, $x \geq 0,y \geq 0\}$ is $\frac{\alpha}{\beta},\alpha,\beta, \in N,gcd(\alpha,\beta) = 1$, then the value of $(\alpha + \beta)$ is :

Accepted Answer

Required area $= \frac{2}{3} 	imes 8 - \frac{1}{2} 	imes \frac{1}{2} 	imes 1$$${= \frac{16}{3} - \frac{1}{4} = \frac{61}{12} = \frac{\alpha}{\beta} }{\Rightarrow \alpha + \beta = 73}$$$$ $$

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