A) Zero
B) \[\frac{1}{3}\]
C) \[\frac{2}{3}\]
D) 1
Correct Answer: C
Solution :
Required area \[=\int_{-1}^{1}{x|x|dx}\]\[=\int_{-1}^{0}{-{{x}^{2}}dx+\int_{0}^{1}{{{x}^{2}}dx}}\] =\[\left( \frac{-{{x}^{3}}}{3} \right)_{-1}^{0}\]\[+\left( \frac{{{x}^{3}}}{3} \right)_{0}^{1}\]\[=\left| \,\frac{-1}{3}\, \right|+\left| \,\frac{1}{3}\, \right|=\frac{2}{3}\].
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