question_answer

Area bounded by the parabola \[{{y}^{2}}=2x\] and the ordinates \[x=1,x=4\] is

A)            \[\frac{4\sqrt{2}}{3}sq.\,unit\]                                        

B)            \[\frac{28\sqrt{2}}{3}sq.\,unit\]

C)            \[\frac{56}{3}\text{ }sq. unit\]                                         

D)            None of these

Correct Answer: B

Solution :

           Required area = \[CDD'C'=2\times ABCD\]                    \[=2\int_{1}^{4}{\sqrt{2}}{{x}^{1/2}}\,dx=\frac{28\sqrt{2}}{3}\] sq. unit.