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The line y = mx bisects the area enclosed by the lines x = 0, y = 0, x = 3/2 and the curve y = 1 + 4x - x². Find the value of 12m.

1. 26
2. 13
3. 39
4. 52

Correct answer: 26

Solution

The total area under the curve from x=0 to x=3/2 is 39/8. The area below y=mx in the same strip is 9m/8. Setting 9m/8 = 39/16 gives m = 13/6, so 12m = 26.

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