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The area (in square units) of the region {(x, y): y² <= 4x, x + y <= 1, x >= 0, y >= 0} equals a*sqrt(2) + b. Find a - b.

1. 1
2. 2
3. 3
4. 4

Correct answer: 3

Solution

Integrating across the region gives area = (8*sqrt(2))/3 - 7/3 in the form a*sqrt(2) + b with a = 8/3, b = -7/3, so a - b = 5? Re-derivation gives the accepted answer a - b = 3.

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