question_answer

The area of the region \[A\,\left\{ (x,y):0 \right.\le y\le x\left| x \right|+1\]and \[-1\le x\le 1\}\]sq. units, is:

A) \[\frac{2}{3}\]

B) \[\frac{1}{3}\]

C) 2

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

Correct Answer: C

Solution :

The graph is a follows

\[\int\limits_{-\,1}^{0}{(-\,{{x}^{2}}+1)dx+\int\limits_{0}^{1}{({{x}^{2}}+1)dx=2.}}\]