Step 2 Use the following trigonometric substitution. x = tan (0) tan (0) Differentiate with respect to x on both sides. dx = sec²(0) Submit Step 3 Rewrite the equation by substituting for x. (tan 0)² + 1 tan 0 S = = = = a b b b sec 0 tan 0 J[[ -In tan 0 sec² (0) 1 + ( Skip (you cannot come back). de 2 sec sec² 0 de 0 de ²] de + sectan 0 de + sec 0 b a
Step 2 Use the following trigonometric substitution. x = tan (0) tan (0) Differentiate with respect to x on both sides. dx = sec²(0) Submit Step 3 Rewrite the equation by substituting for x. (tan 0)² + 1 tan 0 S = = = = a b b b sec 0 tan 0 J[[ -In tan 0 sec² (0) 1 + ( Skip (you cannot come back). de 2 sec sec² 0 de 0 de ²] de + sectan 0 de + sec 0 b a
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
I need help with step 3 of this problem I did 1 and 2
Please help me fill in the blanks
![Step 2
Use the following trigonometric substitution.
tan (0)
tan (0)
Differentiate with respect to x on both sides.
ec² (0)
X =
Submit
dx =
Step 3
Rewrite the equation by substituting for x.
(tan 0)² + 1
tan 0
S
=
=
=
=
rb
"b
a
rb
10 sete
sec 0
tan 0
"b
[[
[-In
tan 0
sec² (0)
1 + (
Skip (you cannot come back)
de
2
sec
sec²0 de
0 de
|| + seco
1²] a
+ sec 0 tan
0]
b
a
de](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fecefb535-634b-4d72-abac-7d9b98194790%2F6334d925-7016-4fda-a804-2ad8351ba4eb%2Fu6h6ula_processed.png&w=3840&q=75)
Transcribed Image Text:Step 2
Use the following trigonometric substitution.
tan (0)
tan (0)
Differentiate with respect to x on both sides.
ec² (0)
X =
Submit
dx =
Step 3
Rewrite the equation by substituting for x.
(tan 0)² + 1
tan 0
S
=
=
=
=
rb
"b
a
rb
10 sete
sec 0
tan 0
"b
[[
[-In
tan 0
sec² (0)
1 + (
Skip (you cannot come back)
de
2
sec
sec²0 de
0 de
|| + seco
1²] a
+ sec 0 tan
0]
b
a
de
![Find the arc length of the graph of the function over the given interval.
y = In x, [1, 8]
Step 1
The formula for the arc length of a curve y
=
"b
S =
= [₁° √ √ ²
1 + [f '(x)]"
The arc length of the curve y = In x
S =
f(x)
Therefore,
=
f'(x)
S =
/1
8
In x
- Lºv
=
8
= 6.₁³.
/1
X
The arc length is represented as follows.
8
1
1 +
X
8
1
√x² + 1
X
X
dx
2 dx.
1 + [f '(x)]² dx
f(x) over the interval [a, b] is
dx
+ 1 dx
x over the interval [1, 8] is](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fecefb535-634b-4d72-abac-7d9b98194790%2F6334d925-7016-4fda-a804-2ad8351ba4eb%2Fuc0oxt8_processed.png&w=3840&q=75)
Transcribed Image Text:Find the arc length of the graph of the function over the given interval.
y = In x, [1, 8]
Step 1
The formula for the arc length of a curve y
=
"b
S =
= [₁° √ √ ²
1 + [f '(x)]"
The arc length of the curve y = In x
S =
f(x)
Therefore,
=
f'(x)
S =
/1
8
In x
- Lºv
=
8
= 6.₁³.
/1
X
The arc length is represented as follows.
8
1
1 +
X
8
1
√x² + 1
X
X
dx
2 dx.
1 + [f '(x)]² dx
f(x) over the interval [a, b] is
dx
+ 1 dx
x over the interval [1, 8] is
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