Calculus this year for me has not been an enjoyable experience and I would appreciate any help with these problems. This is a graded assignment for the end of my 3rd quarter. I would like to end off on a good note so hopefully someone can assist me. Thank you.
1. Find the volume of a solid whose base is enclosed by the circle x^2 + y^2=1, and whose cross sections taken perpendicular to the base are equilateral triangles with bases in the xy-plane.
2. Let R be the region enclosed by the graphs of y=ln(x^2 + 1) and y=cos(x). Setup, using integrals, but do not evaluate the following:
a. The area of R.
b. The base of a solid is region R. Each cross section of the solid perpendicular to the x-axis is an isosceles right triangle. Express the volume of the solid.