Name ___________________________                        BC Calculus                        SHW 1

In Exercises 1-5 , find the volume of the solid obtained by rotating the region specified about the x-axis (disk method).

Exercise 1.   y = x^2 , x = 1,   y = 0.        



                                                                         

Exercise 2.   y = exp(x) , x = 0, x = 1, y = 0.  




Exercise 3.   y = 1/x , x = 1, x = 2, y = 0.  




Exercise 4.   y = sqrt(x-1) , x = 2, x = 5, y = 0.  




Exercise 5.   y = x^2 , 0 <= x and x <= 2, x = 0, y = 4.  




In Exercises 6-10 , find the volume of the solid obtained by rotating the region specified about the y-axis (shell method).

Exercise 6.   y = x^2 , x = 1,   y = 0.                                             



                                    

Exercise 7.   y = exp(x) , x = 0, x = 1, y = 0.  




Exercise 8.   y = 1/x , x = 1, x = 2, y = 0.  




Exercise 9.   y = sqrt(x-1) , x = 2, x = 5, y = 0.  




Exercise 10.   y = x^2 , 0 <= x and x <= 2, x = 0, y = 4.  




In Exercises 11-15 , find the volume of the solid obtained by rotating the region about the given line.

Exercise 11.   y = x , y = sqrt(x),   about the line y = 1.                       



                                                          

Exercise 12.   y = x^2 , y = 4, about the line y = 4. 




Exercise 13.   y = x^4 , y = 1, about the line y = 2. 




Exercise 14.    y = 1/x , y = 0,   x = 1, x = 3,  about the line y = -1. 




Exercise 15. y = x^2 , x = y^2, about the line y = -1.