Question 13.9: Find the area bounded by y = x³ and the x axis from x = −3 t......
Find the area bounded by y = x³ and the x axis from x = −3 to x = −2.
Step-by-Step
Figure 13.11 illustrates the required area.
\begin{aligned}\int_{-3}^{-2} x^3 \mathrm{~d} x & =\left[\frac{x^4}{4}\right]_{-3}^{-2} \\& =\left\{\frac{(-2)^4}{4}\right\}-\left\{\frac{(-3)^4}{4}\right\}=-\frac{65}{4}\end{aligned}
The area is 65/4 square units; the negative sign indicates that it is below the x axis.
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