question_answer

If area of the region bounded by the curves \[y=|1+\{|x|\}|\]and\[3y=|-2{{x}^{2}}+5x+3|\]for \[-\frac{1}{2}<x\le 1,\](where {.} denotes fractional part of x) is A, then \[\frac{72}{17}A\]equals

A)  1                            

B)  4      

C)  2                            

D)  3

Correct Answer: C

Solution :

\[\int\limits_{-1/2}^{0}{\left[ (1-x)-\left( \frac{-2{{x}^{2}}+5x+3}{3} \right) \right]dx}\] \[+\int\limits_{0}^{1}{\left[ \left( \frac{-2{{x}^{2}}+5x+3}{3} \right)-(1+x) \right]dx=\frac{17}{36}sq.units}\]