Final answer:
The area between the curves x=2y² and xy=1 is found by integrating the upper curve minus the lower curve with respects to y, using the y-values of their intersection points as limits.
Step-by-step explanation:
To find the area between the curves x=2y² and xy=1, you first need to find the points of intersection of the two curves. This can be done by equating x from the equation xy=1 and solving for y, then plugging it into the equation x=2y². Once you have the points of intersection, you will set up the integral to calculate the area. In this case, because both equations are functions of y, you would integrate with respect to y. The limits of integration are the y-values of the intersection points. The area is then given by the integral from a to b of the upper curve (derived from x=2y²) minus the lower curve (derived from xy=1).