Let S($\alpha $) = {(x, y) : y2 $ \le $ x, 0 $ \le $ x $ \le $ $\alpha $} and A($\alpha $) is area of the region S($\alpha $). If for a $\lambda $, 0 < $\lambda $ < 4, A($\lambda $) : A(4) = 2 : 5, then $\lambda $ equals

Question

Let S($\alpha $) = {(x, y) : y² $ \le $ x, 0 $ \le $ x $ \le $ $\alpha $} and A($\alpha $) is area of the region S($\alpha $). If for a $\lambda $, 0 < $\lambda $ < 4, A($\lambda $) : A(4) = 2 : 5, then $\lambda $ equals

$2{\left( {{4 \over {25}}} \right)^{{1 \over 3}}}$

$2{\left( {{2 \over {5}}} \right)^{{1 \over 3}}}$

$4{\left( {{4 \over {25}}} \right)^{{1 \over 3}}}$

$4{\left( {{2 \over {5}}} \right)^{{1 \over 3}}}$

Solution

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