Final answer:
The volume of the solid formed by the equations y = x², y = x², and y² = 1 is 0 units cubed.
Step-by-step explanation:
To find the volume of the solid formed by the equations y = x², y = x², and y² = 1, we need to determine the limits of integration. Since the three equations represent parabolas in the xy-plane, the limits of integration will be the x-values where the parabolas intersect. By setting the equations equal to each other, we have x² = x² = 1. This simplifies to x = ±1. Therefore, the limits of integration for the volume calculation are -1 and 1.
Next, we need to determine the cross-sectional area of the solid at each value of x.
This is given by A = y² - (x²)²
Plugging in the value of y from the first equation, we have A = (x²)² - (x²)² = 0.
Therefore, the cross-sectional area is always zero, which means the volume of the solid is also zero.
So, the volume of the solid formed by the given equations is 0 units cubed.