The area bounded by the curve y = x|x|, X-axi | vedclass

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(C) The function $y = x|x|$ is defined as $y = x^2$ for $x \ge 0$ and $y = -x^2$ for $x < 0$.Since we are calculating the area, we take the absolute v

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$2/3$

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(C) The function $y = x|x|$ is defined as $y = x^2$ for $x \ge 0$ and $y = -x^2$ for $x Since we are calculating the area, we take the absolute value of the function: $\int_{-1}^1 |x|x|| dx$.This can be split into two intervals: $\int_{-1}^0 |-x^2| dx + \int_{0}^1 |x^2| dx$.Since $|-x^2| = x^2$ and $|x^2| = x^2$, the integral becomes $\int_{-1}^0 x^2 dx + \int_{0}^1 x^2 dx$.Evaluating the integrals: $[\frac{x^3}{3}]_{-1}^0 + [\frac{x^3}{3}]_{0}^1$.$= (0 - (-1/3)) + (1/3 - 0) = 1/3 + 1/3 = 2/3$.

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

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