What is the area bounded by the curve f(x), the x-axis and the lines x=-2 and x=1?
For the following three (03) items: Consider the function f(x)=x|x|.
- A. \frac{1}{3}
- B. \frac{2}{3}
- C. \frac{5}{2}
- D. 3 ✓
Correct Answer: D. 3
Explanation
The required area is given by \int_{-2}^{1} |f(x)| \,dx = \int_{-2}^{1} |x|x|| \,dx = \int_{-2}^{1} x^2 \,dx. Evaluating the integral yields [\frac{x^3}{3}]_{-2}^{1} = \frac{1}{3} - (\frac{-8}{3}) = \frac{9}{3} = 3.
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