Final answer:
To find the area of the region y² = x²(1 - x²), determine the limits of integration and integrate the equation with respect to x from the two x-values where the curve intersects the x-axis.
Step-by-step explanation:
The equation given is y² = x²(1 - x²). To find the area of the region, we need to determine the limits of integration and then integrate the equation with respect to x. The limits of integration are the x-values at which the curve intersects the x-axis. Setting y = 0, we get x = 0 and x = 1 as the limits of integration.
To integrate y² = x²(1 - x²), we can simplify it to y = x√(1 - x²) and then integrate y with respect to x from x = 0 to x = 1. The integral becomes ∫(0 to 1) x√(1 - x²) dx. Using appropriate substitution or integral techniques, we can evaluate the integral to find the area of the region.