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Find the area in the first quadrant bounded by the parabola y² = 4x, the x-axis, and the normal to the curve drawn at the point (1, 2).

1. 10/3
2. 7/3
3. 4/3
4. 9/2

Correct answer: 10/3

Solution

The normal at (1,2) hits the x-axis at (3,0); summing the parabolic region (x: 0 to 1) and the triangle (x: 1 to 3) gives area 10/3.

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