mat266 6.4.pdf - Binbin Yang Assignment Section 6.4 due...

Binbin Yang Inozemtseva MAT 266 Spring 2019
Assignment Section 6.4 due 01/27/2019 at 11:59pm MST
1. (1 point) Use the Table of Integrals in the back of your
textbook to evaluate the integral:
Z
sec
3
( 5 x ) dx
+ C
Solution:
SOLUTION
From a table of integrals, we have
Z
sec
3
( u ) du =
1
2
sec ( u ) tan ( u )+
1
2
ln sec ( u )+ tan ( u ) + C
For
Z
sec
3
( 5 x ) dx , we let u = 5 x , du = 5 dx = ⇒
1
5
du = dx , and
our integral can be written as
Z
sec
3
( 5 x ) dx =
1
5
Z
sec
3
( u ) du
=
1
5
h
1
2
sec ( u ) tan ( u )+
1
2
ln sec ( u )+ tan ( u )
i
+ C
=
1
10
sec ( 5 x ) tan ( 5 x )+
1
10
ln sec ( 5 x )+ tan ( 5 x ) + C
Correct Answers:
• (1/(2*5))*(sec(5*x)*tan(5*x)+ln(abs(sec(5*x)+tan(5*x))))
2. (1 point) Use the table of in Integrals in the back of your
textbook to evaluate the integral:
Z
p
9 - 4 x - 4 x 2 dx
Note: Use an upper-case ”C” for the constant of integration.
Solution:
SOLUTION
From a table of integrals, we have
Z
p
a 2 - u 2 du =
1
2
u
p
a 2 - u 2 +
1
2
a
2
sin
- 1
u
a
+ C
To evaluate
R
√
9 - 4 x - 4 x 2 dx we need to complete the square
inside the radical to use the above formula.