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Find the area (in square units) of the region A = {(x, y) in R x R: 0 <= x <= 3, 0 <= y <= 4, y <= x² + 3x}.

1. 53/6
2. 59/6
3. 8
4. 26/3

Correct answer: 59/6

Solution

For 0 <= x <= 1 the upper boundary is the parabola, and for 1 <= x <= 3 it is y = 4, giving total area 11/6 + 8 = 59/6.

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