calc 2 exam 1

  1. Evaluate 01x(x2+1)5 dx. Simplify your answers completely. 

  2. Find the total area of the region enclosed by y=x and y=x3-3x.

  3. Find the volume of the region bounded by x=6y-y2 and x=0, rotated about the x-axis.

  4. Find the volume of the region bounded by y=x2, y=4, and x=0 rotated about the y-axis.

  5. A solid is obtained by rotating the region bounded by the curves y=x2 and x=y2 rotated about y=1.

    1. Set up an integral which calculates the volume using the washer method. Do not evaluate the integral.

    2. Set up the integral which calculates the volume using the shell method. Do not evaluate the integral.

  6. Use the disk method to find the formula for the volume of a cone with height H and radius R.

  7. Evaluate the following integrals.

  1. x+13x2+6x-5dx

  2. x22+xdx

8. Find the area of the region bounded by y=x, y=x2, and x=2.

9. Find the volume of the solid obtained by rotating the region bounded by y=(x-2)2 and y=x+10 about the x-axis.

10. A solid is formed by rotating the triangular region with vertices (1,0) and (2, 1) and (1,1) about the y-axis. Find the volume of the solid.

11. Find the volume of the solid obtained by rotating the region bounded by y=(3x-x2) and y=0 about the line x=-1.

12. Use the shell method to find the volume of a cone with base radius R and height H.


13. Evaluate the following integrals.

  1. x1-x2dx

  2. xx-3dx

14. Find the area enclosed between y=x2 and y=8x-x2

15. Find the volume of the region bounded by y=ex, y=0, x=-1, and x=1, rotated about the x-axis.

16. Find the volume of the solid obtained by rotating y=x2, y=x3 about the y-axis.

17. Find the volume of the solid obtained by rotating y=2x2 - x3 and y=0 about the y-axis.

18. Find the volume obtained by rotating the region bounded by y=x2 and y=x about the line x=2.