AP Calculus
Mrs. Pauly
Name:____________________________
REVIEW 7-3/Slope Fields
Use the disks or washers method to determine the volume of the solid obtained by
rotating the region bounded by the given information.
1. y = x, y = 3, y ! axis rotate about the y-axis
2. y = 7 ! x 2 , x = !2, x = 2, x ! axis rotate about the x-axis
3. . x = y 2 ! 6y + 10, x = 5 rotate about the y-axis
4. y = 2x 2 , y = x 3 rotate about the x-axis
5. . x = y 2 ! 4, x = 6 ! 3y rotate about the line x=24
6. Draw a slope field for
dy
1
=
dx 1 + x 2
7. a) Draw a slope field for
dy
= x4 ( y ! 2)
dx
b) Describe all points in the xy-plane for
which the slopes are negative
c) Find the particular solution y=f(x) to the
given differential equation with the initial
condition f(0)=0