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The parabola y = a x² + b x + c passes through (1, 2) and the tangent to it at the origin is the line y = x. Find the area enclosed between the curve, the tangent line, and the vertical line through the minimum point of the curve.

1. 1/24
2. 1/12
3. 1/8
4. 1/6

Correct answer: 1/24

Solution

The curve is y = x² + x with minimum at x = -1/2; between x = -1/2 and 0 the gap to the tangent y = x is x², whose integral is 1/24.

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