A) 8/3 sq. units
B) 10/3 sq. units
C) 11/3 sq. units
D) 11/4 sq. units
Correct Answer: C
Solution :
[c] \[{{y}^{2}}=4[\sqrt{y}]x\] For \[y\in [1,4][\sqrt{y}]=1\]or \[{{y}^{2}}=4x.\] Similarly, for \[x\in [1,4),\left[ \sqrt{x} \right]=1\] and \[{{x}^{2}}=4\left\lfloor \sqrt{x} \right\rfloor y\]would Transform into \[{{x}^{2}}=4y.\] The required area is the shaded region. \[A=\int\limits_{1}^{2}{(2\sqrt{x}-1)dx+\int\limits_{2}^{4}{\left( 2\sqrt{x}-\frac{{{x}^{2}}}{4} \right)dx}}\] \[={{\left( \frac{4}{3}{{x}^{3/2}}-x \right)}_{1}}^{2}+{{\left( \frac{4}{3}{{x}^{3/2}}-\frac{{{x}^{3}}}{12} \right)}_{2}}^{4}=\frac{11}{3}\] Sq. units.You need to login to perform this action.
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