Chapter 6 Review Worksheet
Be sure to use proper notation throughout all of your work. You will lose points if you are missing a dx or
have an integral sign where one does not belong, etc….
1. The slope field for
a)





dy x  1

is
dx
y
b)
c)

d)


































































2. Solve the differential equation below for y. Find the particular solution using the initial condition.
dy 3x2
=
f (0) =1
dx ey
3. Solve the differential equation below for y. Find the particular solution using the initial condition.
dy 5
= , f (-1) = 2
dx y
4. Solve the differential equation below for y. Find the particular solution using the initial condition.
dy
= 4xy, f (1) = -1
dx




Integrate.
5.
ò
dx
xcos 2 (ln x)
6.
2p
8.
ò sin xcos
p
3
2
xdx
9.
ò
2
1
6x2 +8x
dx
x3 + 2x2
ò xln
4dx
2
( 2x)
4
7.
 x (x
2
2
3
 8)2 dx