The area bounded by the curve y = x | x|, x-axis and the ordinates x = –1 and x = 1 is given by ______. [Hint: y = x2 if x 0 and y = –x2 if x

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 = x2 if x > 0 and y = –x2 if x < 0]

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The area bounded by the curve y = x | x|, x-axis and the ordinates x = –1 and x = 1 is given by underline($\frac{2}{3}$). Explanation: When x > 0, |x| = x $\therefore$ Equation of the curve y = x2 When x < 0, |x| = -x Equation of the curve y = -x2 Curve y = x |x|, x $\geq$ -1, x $\leq$ 0 The area bounded by x-axis = Area of ​​region APO + Area of ​​region OBQ `= |int_(-1)^0 - x^2 dx| + int_0^1 x^2 dx = |[-x^$\frac{3}{3}$]|_-1^0 + [x^$\frac{3}{3}$]_0^1 = |-0 - $\frac{1}{3}$| + [$\frac{1}{3}$ - 0] = $\frac{1}{3}$ + $\frac{1}{3}$ = $\frac{2}{3}$` square unit [Solution diagram: 13119_solution_1.png]

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