Problem 2. Gabrieľ's Horn is a three-dimensional surface obtained by rotating the graph y = ! about the x-axis on the interval [1, 00). --2 (a) Find the volume enclosed by Gabriel's Horn. (b) Set up an integral for the surface area of Gabrieľ's Horn. (c) Does the integral in part (b) converge or diverge? Hint: Compare the integral with an appropriate p-integral.

1. (2 points) State the formula for the area of an equilateral triangle with side length a. 2. (13 points) Consider the solid whose base is the region bounded by the curves y = Vx, y = 0 and x = 4, and whose cross-sections perpendicular to the x-axis are equilateral triangles. (a) (8 points) Use the slicing method to write an integral representing the volume of this solid. (b) (5 points) Find the volume by evaluating the above integral.

dx. B. (i) Evaluate - tan (ii) Find the volume generated by revolving the curve' between the limits x-0 to x -1,about the x-axis.