question_answer

The area of the region (in the square unit) bounded by the curve \[{{x}^{2}}=4y,\] line \[x=2\] and x-axis is         [MP PET 2002]

A)            1    

B)            \[\frac{2}{3}\]

C)            \[\frac{4}{3}\]                      

D)            \[\frac{8}{3}\]

Correct Answer: B

Solution :

                   Given \[{{x}^{2}}=4y\]                    Shaded area \[=\int_{0}^{2}{\frac{{{x}^{2}}}{4}dx}\]\[=\frac{1}{12}[{{x}^{3}}]_{0}^{2}=\frac{8}{12}=\frac{2}{3}\].