MAT266_Test_1_rev - 1 MAT 266 Test 1 Review Techniques of...

1
MAT 266 Test 1 Review
Techniques of integration and improper integrals, sections 5.5, 6.1-6.4 and 6.6 in
Essential Calculus, Early Transcendentals , 2
nd
Edition, by James Stewart.
Find the following indefinite integrals (1-21).
1.
∫
(ln x )
5
5 x
dx 2.
∫
2 sin( x )
1 + cos 2 ( x )
dx 3.
∫
3 x + 5
5 x 2 - 4 x - 1
dx
4.
∫
1
x
2
√
16 - x
2
dx 5.
∫
x
2
√
5 + x
dx 6.
∫
10 ze
3 z
dz
7.
∫
t
6
ln( t ) dt 8.
∫
2 x
2
+ 6
( x + 1)( x 2 + 1)
dx 9.
∫
x + 1
x 2 + 1
dx
10.
∫
5 x cos(2 x ) dx 11.
∫
1
x 2
√
x 2 - 49
dx 12.
∫
2 x + 3
x ( x 2 - 6 x + 9)
dx
13.
∫
cos
2
(3 θ ) dθ 14.
∫
sec
7
( x ) tan
3
( x ) dx 15.
∫
sec
4
( t ) tan
2
( t ) dt
16.
∫
cos
3
(
x
2
)
dx 17.
∫
sin
5
( x ) cos
2
( x ) dx 18.
∫
x
3
√
x 2 + 1
dx
19.
∫
arctan( x ) dx 20.
∫
10
(9 + x 2 ) 3 / 2
dx 21.
∫
sin
- 1
( x ) dx
Find the exact value of the definite integrals (22-24).
22.
∫
2
0
(9 - 2 t )
3 / 2
dt 23.
∫
2
0
e
x
1 + e 2 x
dx 24.
∫
3
0
x
√
4 - x dx
25. Find the average value of the given function on the given interval.
)
on [0 , 3]
Use the table of integrals in the back of your textbook to find the following indefinite integrals (26-28):