A) zero
B) \[\frac{1}{3}\]
C) \[\frac{2}{3}\]
D) 1
Correct Answer: C
Solution :
The area of the region bounded by the curve \[y=f(x)\] and the ordinates \[\operatorname{x} = a, \,x = b\] is given by \[Area=\left| \int{_{a}^{b}\,y\,dx} \right|\] According to the question, \[y=x\left| x \right|=\left\{ \begin{matrix} {{x}^{2}},\,\,x\ge 0 \\ -\,{{x}^{2}},\,\,x<0 \\ \end{matrix} \right.\] Required area \[= area of region OAB + area of region OCD\] \[= 2 \times Area of region OAB\] \[=\,\,\,2\int_{0}^{1}{{{x}^{2}}dx=\frac{2}{3}}\,sq.units\]You need to login to perform this action.
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