Let f denote the area of the region in the first quadrant bounded by x = 0 , x = 1 , y 2 = x and y = | x - 5 | - | 1 - x | + x 2 . Then ( f ( 0 ) + f ( 1 ) ) is equal to [2026]

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Solution

Q.
Let $f (α)$ denote the area of the region in the first quadrant bounded by $x = 0$ , $x = 1$ , $y^{2} = x$ and $y =$ $| α x - 5 |$ $-$ $| 1 - α x |$ $+ α x^{2} .$ Then $(f (0) + f (1))$ is equal to [2026]

1 9

2 12

3 7

4 14

Ans.
(3)

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