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Question:

If the area (in sq. units) of the region (x,y): y² ≤ 4x, x + y ≤ 1, x ≥ 0, y ≥ 0 is a² + b, then a - b is equal to?

6

83

103

-2;3

Solution:

Correct option is C. 6
(x,y): y² ≤ 4x, x + y ≤ 1, x ≥ 0, y ≥ 0
A = ∫₀^(3-√2)/2 √(4x) dx + 1/2(1 - (3 - √2)/2)(1 - (3 - √2)/2) = 2[x³/²]₀^((3-√2)/2) / (3/2) + 1/2((√2 - 1)/2)((√2 - 1)/2) = 8/3√2 + (-1/3)
a = 8/3, b = -1/3
a - b = 6.