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

Question

Dr. Abubacker · Accepted Answer

(c)
$Required\ area = \left| \int_{- 1}^{1}{x|x|}dx \right|$
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$= \left| \int_{- 1}^{0}{x|x|}dx \right| + \int_{0}^{1}{x|x|dx}$
$= \left| \int_{- 1}^{0}{- x^{2}}dx \right| + \int_{0}^{1}{x^{2}dx}$
$= \left| \left\lbrack \frac{- x^{3}}{3} \right\rbrack_{- 1}^{0} \right| + \left\lbrack \frac{x^{3}}{3} \right\rbrack_{0}^{1} = \frac{1}{3} + \frac{1}{3} = \frac{2}{3}$

Q. The area bounded by the curve$\ y = x|x|,$ $x$-axis and the ordinates $x = 1,\ x = - 1$ is given by

Explanation

Reviewed by Dr. Abubacker

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