The following integral can be evaluated by using substitution: a) b) Identify the inside function. u= x^4+1 Differentiate: 4x^3 47³ Make dr the subject: dz Rewrite the whole integral in terms of u and du: f Simplify and cancel I's: Integrate with respect to u: 3/2 149 3 N/W * du +1 ✔ 149 x √= 3x^3 sqrt(u) 3x³ √2¹ +1 dz du 4x^3

The following integral can be evaluated by using substitution: a) b) Identify the inside function. u= x^4+1 Differentiate: 4x^3 47³ Make dr the subject: dz Rewrite the whole integral in terms of u and du: f Simplify and cancel I's: Integrate with respect to u: 3/2 149 3 N/W * du +1 ✔ 149 x √= 3x^3 sqrt(u) 3x³ √2¹ +1 dz du 4x^3

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

answer part A last part ,tow part in part b and part c . thanks

c)
Hence write down the indefinite integral:
(Don't forget the constant of integration as this is an indefinite integral.)
32³
1¹ +1
dz

The following integral can be evaluated by using substitution:
a)
b)
Identify the inside function. u= x^4+1 I¹ +
Differentiate:
4x^3
Make de the subject: dx =
Rewrite the whole integral in terms of u and du: f
Simplify and cancel z's: 3/2
Integrate with respect to u:
149
* du
149 *
3x³
√2¹ +1
1=
3x^3
sqrt(u)
dz
du
4x^3

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Follow-up Question

can you help me with the parts i got wrong . thanks

c)
Hence write down the indefinite integral:
-5 ln (42) dr
(Don't forget the constant of integration as this is an indefinite integral.)
5x-5x 1n(4x)+c 5x -5x ln(4x) + c *

The following integral may be evaluated by using integration by parts.
Notes:
• powers can be entered using ^
to divide, use /
a)
du
The product-5 In(4x) must be written in the form u
Determine u,and u:
b)
Apply the integration by parts formula:
U=
V=
fudr =
fudr =
In(4x)
-5X
-5 ln(42) dz
uv
>>
뿜
1/X
-5
Rie
- S
X -S -5
>>
>
dz
dr

Solution

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