Area of the region bounded by the curve y = x | vedclass

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(A) The area $A$ is given by the integral of the absolute value of the function $y = x^3$ from $x = -1$ to $x = 2$.$A = \int_{-1}^{2} |x^3| dx$Since $

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$17$

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(A) The area $A$ is given by the integral of the absolute value of the function $y = x^3$ from $x = -1$ to $x = 2$.$A = \int_{-1}^{2} |x^3| dx$Since $x^3 \le 0$ for $x \in [-1, 0]$ and $x^3 \ge 0$ for $x \in [0, 2]$, we split the integral:$A = \int_{-1}^{0} (-x^3) dx + \int_{0}^{2} x^3 dx$$A = [-\frac{x^4}{4}]_{-1}^{0} + [\frac{x^4}{4}]_{0}^{2}$$A = (0 - (- \frac{(-1)^4}{4})) + (\frac{2^4}{4} - 0)$$A = (0 - (-1/4)) + (16/4 - 0)$$A = 1/4 + 4 = 17/4$.

Area of the region bounded by the curve $y = x^3$, $x$-axis and the ordinates $x = -1$ and $x = 2$ is . . . . . . . (in $/4$)

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