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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?
- Area(R) = c³/6
- Area(R) = c³/3
- lim c->0+ Area(T)/Area(R) = 3
- 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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