Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.1: Verifying Trigonometric Identities
Problem 65E
Related questions
Question
![25
Evaluate the integral:
dx
x2 + 64
(A) Which trig substitution is correct for this integral?
O x =
8 tan(0)
64 tan(0)
O x =
8 sin(0)
O x =
64 sin(0)
х — 25 sec(Ө)
64 sec(0)
(B) Which integral do you obtain after substituting for x and simplifying?
Note: to enter 0, type the word theta.
do
(C) What is the value of the above integral in terms of 0?
+ C
(D) What is the value of the original integral in terms of x?
+ C](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6fbbd54-11e1-4a6d-a978-4b2d538524c1%2F1d4d7b6e-c0ae-4fad-a076-0b5ff39f7057%2F6n24i1_processed.png&w=3840&q=75)
Transcribed Image Text:25
Evaluate the integral:
dx
x2 + 64
(A) Which trig substitution is correct for this integral?
O x =
8 tan(0)
64 tan(0)
O x =
8 sin(0)
O x =
64 sin(0)
х — 25 sec(Ө)
64 sec(0)
(B) Which integral do you obtain after substituting for x and simplifying?
Note: to enter 0, type the word theta.
do
(C) What is the value of the above integral in terms of 0?
+ C
(D) What is the value of the original integral in terms of x?
+ C
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1
Given that :
The integral is .
Step 2
By using formulae,
tan2 x + 1 = sec2 x.
Step 3
To find the integral :
By using substitution.
Substitute x = 8 tan , then dx = .
Then,
Step 4
Step by step
Solved in 8 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
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