The base of a solid is bounded by the curve y=√ x + 1, the x-axis and the line x = 1. The cross sections, taken perpendicular to the x-axis, are squares. Find the volume of the solid.

Answer 1

this is similar to another one.
I assume you mean y = √(x+1) otherwise the boundary is not closed.
The base of each square is just y. So, since each square patch has thickness dx, the sum of their volumes is just
∫[-1,1] y^2 dx = ∫[-,1] (x+1) dx

Answer 2

extra credit: what if the cross-sections are parallel to the x-axis?

Answer 3

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