The following integral can be evaluated by using substitution: a) Identify the inside function. = x^3+15x + 15z 3z² + 15 Differentiate: Factorise this: 3x^2+15 = 3 [4 (2²+5) (2³ +152)³ dr X^2+5

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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answer part B where i got wrong and part D

d
0
d
3
d
O
d
O
d
d
O
d
O
d
O
d
8
ū
d)
Hence write down the indefinite integral:
[4 (2²+5) (2³ +152)³ dr
(Don't forget the constant of integration as this is an indefinite integral.)
Show steps (Your score will not be affected.)
3
Answer: 1/3(x^3+15x)^4+C (x³ + 15z)¹ +c ✔
Evaluate the definite integral, correct to 4 significant figures:
Your ans
You scor
4 (2²+5) (2³ + 15z)³ dz
Transcribed Image Text:d 0 d 3 d O d O d d O d O d O d 8 ū d) Hence write down the indefinite integral: [4 (2²+5) (2³ +152)³ dr (Don't forget the constant of integration as this is an indefinite integral.) Show steps (Your score will not be affected.) 3 Answer: 1/3(x^3+15x)^4+C (x³ + 15z)¹ +c ✔ Evaluate the definite integral, correct to 4 significant figures: Your ans You scor 4 (2²+5) (2³ + 15z)³ dz
The following integral can be evaluated by using substitution:
a)
b)
Identify the inside function, u = x^3+15x 3 + 15z
3x² + 15
Differentiate:
Factorise this:
=
3x^2+15
3
X^2+5
Rewrite the whole integral in terms of u and du: f
Simplify and cancel z²+5: 4/3 u^3
Integrate with respect to u: 1/3 u^4+c
[4 (2²+5) (2³ +152)³ dr
+00
4(x^2+5)u^3
du
+c x
3
✓
du
X^2+5
>
>
>
>
Ga
5 5 9 5 25 25 2
Yc
Ga
Ga
Ga
Yc
Yc
Transcribed Image Text:The following integral can be evaluated by using substitution: a) b) Identify the inside function, u = x^3+15x 3 + 15z 3x² + 15 Differentiate: Factorise this: = 3x^2+15 3 X^2+5 Rewrite the whole integral in terms of u and du: f Simplify and cancel z²+5: 4/3 u^3 Integrate with respect to u: 1/3 u^4+c [4 (2²+5) (2³ +152)³ dr +00 4(x^2+5)u^3 du +c x 3 ✓ du X^2+5 > > > > Ga 5 5 9 5 25 25 2 Yc Ga Ga Ga Yc Yc
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