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

Question

Accepted Answer

Correct answer: C. (c) For =0 : curve is y=5-1=4 (horizontal line), area = _0^1 (4- x ) dx=4- 23= 103 For =1 and 0 x 1 : |x-5 |=5-x , |1-x |=1-x, so y=4+x^2 Area = _0^1 0.05em(4+x^2- x) dx=4+ 13- 23= 113 f (0 )+f (1 )= 103+ 113=7

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

Solution

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