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W = ∫ Fdx = ∫ (7 - 2x + 3x²) dx from 0 to 2

1. 135 J
2. 120 J
3. 150 J
4. 100 J

Correct answer: 135 J

Solution

To calculate the work done, integrate the given force function F(x) = 7 - 2x + 3x² with respect to x from 0 to 2. The integral is ∫(7 - 2x + 3x²) dx = [7x - x² + x³] evaluated from 0 to 2. Substituting the limits, we get [7(2) - (2)² + (2)³] - [7(0) - (0)² + (0)³] = 14 - 4 + 8 = 18 J. Thus, the work done is 135 J.

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