Final answer:
The volume of the solid is obtained by integrating the area of the square cross-sections, which is (5 - x^2)^2, from -√5 to √5.
Step-by-step explanation:
The volume of a solid with a base bounded by y = x2 and y = 5, and with square cross-sections perpendicular to the x-axis, can be found by integrating the area of the squares along the x-axis. The limits of integration will be the x-values where the parabola y = x2 intersects the line y = 5. These x-values are obtained by solving the equation x2 = 5, which gives us x = √5 and x = -√5. At any point x between these limits, the side of a square cross-section is the distance between the parabola and the line, which is 5 - x2. Therefore, the area of a cross-section is (5 - x2)2. The volume is then the integral from -√5 to √5 of (5 - x2)2 dx.