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Let T be the triangle with vertices (0, 0), (0, c²) and (c, c²), and let R be the region between the line y = cx and the curve y = x², with c > 0. Which statement is correct?

1. Area(R) = c³/6
2. Area(R) = c³/3
3. lim c->0+ Area(T)/Area(R) = 3
4. lim c->0+ Area(T)/Area(R) = 3/2

Correct answer: Area(R) = c³/6

Solution

The region between y = cx and y = x² from x = 0 to x = c has area integral(cx - x²)dx = c³/2 - c³/3 = c³/6.

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