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A horizontal line y = c passes through the point (b, c) and meets the curve y = 8x - 27x³. If the two shaded regions formed are of equal area, determine b and c.
- b = 1/9, c = 23/27
- b = 4/9, c = 23/27
- b = 1/3, c = 32/27
- b = 2/3, c = 32/27
Correct answer: b = 1/3, c = 32/27
Solution
Requiring the two areas equal forces integral₀^b (8x - 27x³ - c) dx = 0 together with c = 8b - 27b³; solving gives b = 1/3 and c = 32/27.
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