The base of a solid is bounded by the curve , 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.

Question

The base of a solid is bounded by the curve , 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.

A.  1 

B. 2 

C. 2.333 

D. None of these

Answer 1

Draw a diagram to verify that the lower bound of integration is x = -1.

We need to integrate the cross-sectional area over the interval [-1 ,1] to get the requested volume:

∫_-1¹ (√x+1)²dx

= ∫_-1¹ (x+1)dx

1/2x² + x ]_-1¹ = 3/2 - (-1/2) = 2