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A curve y = f(x) has slope 2x + 1 at every point (x, f(x)) and passes through (1, 2). Find the area of the region bounded by the curve, the x-axis and the line x = 1.
- 5/6
- 6/5
- 1/6
- 1
Correct answer: 5/6
Solution
Integrating gives y = x² + x, which crosses the x-axis at x = 0 (in the relevant range). The area from x = 0 to x = 1 equals integral of (x² + x) dx = 5/6.
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