2.6 Higher - Order Derivatives and Implicit Differentiation
Find y ' , y ' , y '
1.
y (3 2 x)7
2.
y
[ y ' 14(3 2 x)6 ; y ' 168(3 2 x)5 ; y ' 1680(3 2 x) 4 ]
6
( x 1) 2
[ y ' 12( x 1)3 ; y ' 36( x 1)4 ; y ' 144( x 1)5 ]
[ y'
10 38 28 10
1 32 1 4
2 5 4 7
x
Using the Definite Integral to find Areas and Volumes of Revolution
1) Find the area enclosed between the following curves
a ) y cos 2 x , y 0 , x
b) y sec2 x , y 2 , x
,x
4
2
,x
4
4
c) y x 2 , y x 2
d ) y 2x x2 , y 0
2) Find the volume of the solid t
Using the Definite Integral to Solve Area Problems
Find the area of the region R specified. It is helpful to make a sketch of the region.
1
1. Bounded by y= 4 , y=0, x=0, and x=1.
[5 sq. units]
2. Bounded by y= 2 -4x, and below x-axis.
[ 3 sq. units]
3. B
3.3 Evaluate the following indefinite integrals using the method of substitution
3x
1.
2.
6(2 x + 3)(x
3.
e
4.
xe
5.
e
6.
7.
x
8.
tan x ln(cos x)dx
9.
cos(ax) sin
10.
sec ( x) tan ( x)dx
11.
csc (3x) cot
12.
ln 3 t
t dt
13.
sec (2 x) tan(2 x)dx
14