A) 6
B) \[\frac{1}{3}\]
C) \[\frac{2}{3}\]
D) None of these
Correct Answer: C
Solution :
Required area \[=\left| \int_{-1}^{1}{x|x|dx} \right|\] \[=\left| \int_{-1}^{0}{x|x|dx} \right|+\int_{0}^{1}{x}|x|dx\] \[=|\int_{-1}^{0}{-{{x}^{2}}dx}|+\int_{0}^{1}{{{x}^{2}}}dx\] \[=\left| \left[ \frac{-{{x}^{3}}}{3} \right]_{-1}^{0} \right|+\left[ \frac{{{x}^{3}}}{3} \right]_{0}^{1}=\frac{1}{3}+\frac{1}{3}=\frac{2}{3}\]You need to login to perform this action.
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