area of the finite region bounde by the graphs of yx2 xy2 an

area of the finite region bounde by the graphs of y=x^2, x+y=2, and y=0

Solution

Point of intersection of y=x^2 and x+y=2 is (1,1)

Therefore, area bounded = integral of x^2 (with x ranging from 0 to 1) + integral of 2-x (with x ranging from 1 to 2)

= (x^3/3)₀¹ + (2x - x^2/2)²₁

= 5/6