Let f( ) denote the area of the region in the first quadrant bounded by x=0, x=1, y²=x and y=| x-5|-|1- x|+ x² . Then (f(0)+f(1)) is equal to

Step-by-step solution

For = 0 : curve is y = 5 - 1 = 4 (horizontal line), area = ₀^1 (4 - x ) dx = 4 - 2 3 = 10 3 For = 1 and 0 x 1 : |x-5| = 5-x , |1-x| = 1-x , so y = 4 + x^2 Area = ₀^1 (4 + x^2 - x ) dx = 4 + 1 3 - 2 3 = 11 3 f(0) + f(1) = 10 3 + 11 3 = 7