JEE-Advanced 2015 (20.D/40)

Calculus Level 4

Suppose that \(F(\alpha)\) denotes the area of the region bounded by \(x=0, \ \ x=2, \ \ y^2=4x\) and \(y=|\alpha x-1|+|\alpha x -2| +\alpha x\), where \(\alpha \in \{ 0,1 \}\).Find the value(s) of \(F(\alpha)+\frac{8\sqrt2}{3}\), when \(\alpha=0\) and \(\alpha=1\). \[\begin{array}{} (1) \, 1 \quad \quad \quad \quad \quad \quad \quad \quad & (2) \, 2 \\ (3) \, 6 & (4) \, 5 \end{array}\] Note :

  • Submit your answer as the increasing order of the serial numbers of all the correct options.

  • For eg, if your answer is \((1),(2)\), then submit 12 as the correct answer, if your answer is \((2),(3),(4)\), then submit 234 as the correct answer.

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