The area (in sq. units) of the region enclosed by (x, y) y x^2, xy 8, y 1 is...

Step-by-step solution

The region is bounded by the curves y = x^2 , xy = 8 , and y = 1 in the first quadrant (as the area must be finite). To find the intersection points of the curves: Intersection of y = x^2 and xy = 8 : x(x^2) = 8 x^3 = 8 x = 2 At x = 2 , y = 4 . Intersection of y = x^2 and y = 1 : x^2 = 1 x = 1 (taking x > 0 ). Intersection of xy = 8 and y = 1 : x(1) = 8 x = 8 . The area can be calculated by integrating with respect to y from y = 1 to y = 4 . For a given y , the value of x ranges from the parabola x = y to the hyper