Question

The area bounded by the curve $y=x|x|$,$x$-axis and the ordinates $x=–1$ and $x=1$ is given by
[Hint:$y=x^2\, if\, x>0$ and $y=–x^2$ if $x<0]$

• A. 0
• B. $\frac{1}{3}$
• C. $\frac{2}{3}$
• D. $\frac{4}{3}$

Answer 1

Answer: (C)

$\frac{2}{3}$

Answer 2

The correct answer is:$\frac{2}{3}units$

Required area$=∫^1_{-1}ydx$
$=∫^1_{-1}x|x|dx$
$=∫^0_{-1}x^2dx+∫^1_0x^2dx$
$=[\frac{x^3}{3}]^0_{-1}+[\frac{x^3}{3}]^1_0$
$=-(-\frac{1}{3})+\frac{1}{3}$
$=\frac{2}{3}units$
Thus,the correct answer is C.