What is the volume of the solid whose cross-sections are equilateral triangles perpendicular to the x -axis and with bases on the region bounded by curves y = x 2 + 1 , x = 1 , and x -axis and the y -axis ?

The volume is the sum of all the areas of the cross-sections.


The Area is the area of an equilateral triangle, where the length of the base is distance from curve 'x^2 + 1' and x-axis.
The height of an equilateral triangle is
 

Therefore Area of triangle is:


Now integrate to find Volume