What is the area bounded by the function f(x) and the x-axis?
Consider the following for the two (02) items that follow : Let the function f(x)=x^{2}-1.
- A. 1/3 square unit
- B. 2/3 square unit
- C. 4/3 square units ✓
- D. 2 square units
Correct Answer: C. 4/3 square units
Explanation
The curve x^2-1 intersects the x-axis at x=-1 and x=1. Since it lies below the x-axis in this interval, the area is \int_{-1}^{1} -(x^2-1)\,dx = -[\frac{x^3}{3} - x]_{-1}^{1} = -(-2/3 - 2/3) = 4/3 square units.
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