(C) The curve is defined as $y = x|x|$.For $x \ge 0$,$y = x^2$.For $x < 0$,$y = -x^2$.The area $A$ is given by the integral $\int_{-1}^{1} |y| dx$.Sin

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(C) The curve is defined as $y = x|x|$.For $x \ge 0$,$y = x^2$.For $x The area $A$ is given by the integral $\int_{-1}^{1} |y| dx$.Since the function $y = x|x|$ is an odd function,the area is $2 \int_{0}^{1} x^2 dx$.$A = 2 \left[ \frac{x^3}{3} \right]_{0}^{1} = 2 \left( \frac{1}{3} - 0 \right) = \frac{2}{3}$.Thus,the required area is $\frac{2}{3}$ square units.

Class 12 Mathematics Application of Integration Area bounded by region of single curve

Medium

The area of the region bounded by the curve $y = x|x|$,the $x-$axis,and the ordinates $x = 1$ and $x = -1$ is given by:

A
$0$
B
$\frac{1}{3}$
C
$\frac{2}{3}$
D
$1$

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Area bounded by region of single curve

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The area of the region bounded by the curve $y = x|x|$,the $x-$axis,and the ordinates $x = 1$ and $x = -1$ is given by:

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