CK-12-Calculus

http://www.ck12.org Chapter 5. Applications of Definite Integrals

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/573

Together these videos show how both methods can be used to solve the same problem (though it’s not always done
this easily!).

Review Questions

In problems #1 - 4, find the volume of the solid generated by revolving the region bounded by the curves about the
x−axis.

1.y=

√

9 −x^2 ,y= 0

2.y= 3 +x,y= 1 +x^2

3.y=secx,y=

√

2 ,−π/ 4 ≤x≤π/ 4

4.y= 1 ,y=x,x= 0

In problems #5–8, find the volume of the solid generated by revolving the region bounded by the curves about the
y−axis.

5.y=x^3 ,x= 0 ,y= 1

6.x=y^2 ,y=x− 2

7.x=cscy,y=π/ 4 ,y= 3 π/ 4 ,x= 0

8.y= 0 ,y=√x,x= 4

In problems #9–12, use cylindrical shells to find the volume generated when the region bounded by the curves is
revolved about the axis indicated.

9.y=^1 x,y= 0 ,x= 1 ,x= 3 ,about they−axis

10.y=x^2 ,x= 1 ,y= 0 ,about thex−axis

11.y= 2 x− 1 ,y=− 2 x+ 3 ,x= 2 ,about they−axis

12.y^2 =x,y= 1 ,x= 0 ,about thex−axis.

13. Use the cylindrical shells method to find the volume generated when the region is bounded byy=x^3 ,y=
    1 ,x=0 is revolved about the liney= 1.