Find the following indefinite integrals:
a)
x10 − 8x6 − 28
2x7
dx∫
x
10
-8x
6
-28
2x
7
dx
ò
b)
12x−2/3 + 4e12x − 5( )dx∫
12x
-2/3
+4e
12x
-5
( )
dx
ò
Determine where the following function is continuous:
f x( ) = 108− 4x
3
2x3 − 32x
fx
()
=
108-4x
3
2x
3
-32x
Find the area enclosed by the curves
f x( ) = x3
fx
()
=x
3
and
g x( ) = 6x2
gx
()
=6x
2
.
Find the absolute maximum and minimum values of
f x( ) = x4 − 8x3 − 32x2
fx
()
=x
4
-8x
3
-32x
2
on the interval [-3, 2].
Evaluate the following definite integrals:
9 x
2
+
6
x
⎛
⎝⎜
⎞
⎠⎟
dx
4
16
∫
9x
2
+
6
x
æ
è
ç
ö
ø
÷
dx
4
16
ò
Find the intervals where
h x( ) = x4 − 2x3 − 72x2 − 8x + 2
hx
()
=x
4
-2x
3
-72x
2
-8x+2
is concave up and concave down.
Find all critical points of
f x( ) = −9x4 + 32x3 −16
fx
()
=-9x
4
+32x
3
-16
and classify each as a relative minimum, relative maximum, or neither one.
Find the average rate of change of
h x( ) = −2x4 + 21x2 − 9
hx
()
=-2x
4
+21x
2
-9
between x = -2 and x = 4.
Find the intervals where
g x( ) = 2 3x −1( )4/3
gx
()
=23x-1
()
4/3
is increasing and the intervals where it is decreasing.
Find the instantaneous rate of change of
f x( ) = x
2 − 8
3x + 4
fx
()
=
x
2
-8
3x+4
at x = -3.
...
Find the following indefinite integralsa) x10 − 8x6.docx
1. Find the following indefinite integrals:
a)
x10 − 8x6 − 28
2x7
dx∫
x
10
-8x
6
-28
2x
7
dx
ò
b)
12x−2/3 + 4e12x − 5( )dx∫
12x
-2/3
+4e
12x
-5
( )
2. dx
ò
Determine where the following function is continuous:
f x( ) = 108− 4x
3
2x3 − 32x
fx
()
=
108-4x
3
2x
3
-32x
Find the area enclosed by the curves
f x( ) = x3
fx
()
=x
3
and
g x( ) = 6x2
gx
3. ()
=6x
2
.
Find the absolute maximum and minimum values of
f x( ) = x4 − 8x3 − 32x2
fx
()
=x
4
-8x
3
-32x
2
on the interval [-3, 2].
Evaluate the following definite integrals:
9 x
2
+
6
x
5. =x
4
-2x
3
-72x
2
-8x+2
is concave up and concave down.
Find all critical points of
f x( ) = −9x4 + 32x3 −16
fx
()
=-9x
4
+32x
3
-16
and classify each as a relative minimum, relative maximum, or
neither one.
Find the average rate of change of
h x( ) = −2x4 + 21x2 − 9
hx
()
=-2x
6. 4
+21x
2
-9
between x = -2 and x = 4.
Find the intervals where
g x( ) = 2 3x −1( )4/3
gx
()
=23x-1
()
4/3
is increasing and the intervals where it is decreasing.
Find the instantaneous rate of change of
f x( ) = x
2 − 8
3x + 4
fx
()
=
x
2
-8
3x+4
