question_answer

The area bounded by the curve \[y={{(x+1)}^{2}},\,y={{(x-1)}^{2}}\] and the line \[y=\frac{1}{4}\] is                                           [IIT Screening 2005]

A)            1/6

B)            2/3

C)            1/4

D)            1/3

Correct Answer: D

Solution :

           Required area \[\left. =2\left| \int_{1/4}^{1}{(\sqrt{y}-1)\ dy} \right. \right|\],(From the symmetry)            On solving, we get required area \[=\frac{1}{3}\] sq. unit.