Integration: Using a Table of Integrals 2

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Ben McGovern

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Christian Lawson-Perfect 2 years, 6 months ago

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Ben McGovern 4 years ago

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Ben McGovern 4 years, 8 months ago

Created this as a copy of Differentiation: Using a Table of Derivatives 2.

Name	Status	Author	Last Modified
Differentiation: Using a Table of Derivatives 2	Ready to use	Ben McGovern	26/09/2022 12:10
Differentiation: Using a Table of Derivatives 3	Ready to use	Ben McGovern	26/09/2022 12:11
Differentiation: Using a Table of Derivatives 4	Ready to use	Ben McGovern	26/09/2022 12:11
Differentiation: Using a Table of Derivatives 5a	Ready to use	Ben McGovern	26/09/2022 12:11
Differentiation: Using a Table of Derivatives 5b	Ready to use	Ben McGovern	26/09/2022 12:12
Differentiation: Using a Table of Derivatives 5c	Ready to use	Ben McGovern	26/09/2022 12:12
Differentiation (Harder powers - negative and fractions) 2	Ready to use	Ben McGovern	04/05/2023 05:42
Differentiation: Stationary Points and their Nature 1	Ready to use	Ben McGovern	26/09/2022 11:56
Differentiation: Stationary Points and their Nature 2	Ready to use	Ben McGovern	26/09/2022 11:56
Integration: Using a Table of Integrals 2	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: Using a Table of Integrals 3a	Ready to use	Ben McGovern	13/02/2023 10:37
Integration: Using a Table of Integrals 3b	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: Using a Table of Integrals 4	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: Using a Table of Integrals 5a	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: Using a Table of Integrals 5b	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: Using a Table of Integrals 5c	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: Using a Table of Integrals 6	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: By Substitution 1a i	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: By Substitution 1b	Ready to use	Ben McGovern	23/02/2023 12:45
Integration: By Substitution 1c	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: By Substitution 2a	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: By Substitution 2b	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: By Substitution 2c	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: By Substitution 3a i	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: By Substitution 3c	Ready to use	Ben McGovern	27/09/2022 09:01
Integration (Negative and Fractional Powers) 2	Has some problems	Ben McGovern	27/09/2022 09:01
Integration (Negative and Fractional Powers) 3	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: Definite Integrals 2	Ready to use	Ben McGovern	26/09/2022 12:18
Integration: By Substitution 1a ii (Negative and Fractional Powers)	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: By Substitution 3a ii (Negative and Fractional Powers)	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: Definite Integrals 3	Ready to use	Ben McGovern	26/09/2022 12:18
Integration: Definite Integrals 4	Ready to use	Ben McGovern	26/09/2022 12:19
CB2 Differentiating polynomials 2	Ready to use	Mash Sheffield	17/04/2025 09:02
CD3 Integration - Substitution	Ready to use	Andrew Neate	17/04/2025 09:02
CB4 Definite integration	Ready to use	Andrew Neate	17/04/2025 09:02
CB6 Differentiating Trig 1	Ready to use	Andrew Neate	17/04/2025 09:02
CB7 Differentiating Trig 2	Ready to use	Andrew Neate	17/04/2025 09:02
CB8 Differentiating with Trig 3	Ready to use	Andrew Neate	17/04/2025 09:02
CB9 Differentiating with Exponentials	Ready to use	Andrew Neate	17/04/2025 09:02
CB10 Differentiation with logs	Ready to use	Andrew Neate	17/04/2025 09:02
CB3 - Indefinite integration - polynomials	Ready to use	Andrew Neate	17/04/2025 09:02
CB5 - Finding turning points	Ready to use	Andrew Neate	17/04/2025 09:02

There are 151 other versions that do you not have access to.

Question statement

Find the integral of $f(x)=\simplify[unitFactor, unitPower, fractionNumbers]{{a_1}*x^{b_1}+{a_2}*x^{b_2}+{a_3}*x^{b_3}}$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

			Name	Type	Generated Value

a_1	integer	4
a_2	integer	10
a_3	integer	-5
b_1	integer	5
b_2	integer	4
b_3	integer	2
advice	string	<p>So, for the function \[y=\s
advice2	string	<p>So, for the function \[y=\s
advice3	string	<p>So, for the function \[y=\s
solutiona	string	<p>So, for the function \[y=\s
solutionb	string	<p>So, for the function \[y=\s
solutionc	string	<p>So, for the function \[y=\s
solutiond	string	<p>So, for the function \[y=\s

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Value

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Generated value: `integer`

→ Used by:

solutiona
solutionb
solutionc
solutiond

Statement
Advice
"Unnamed part" → "Gap 0" - Correct answer

Parts

Gap-fill
1. Gap Gap 0 Mathematical expression
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Gap 0

Advice

From the Table of Integrals we see that a function of the form

$f(x)=x^n$ has the integral

$\int x^n dx = \frac{x^{n+1}}{n+1}+ c,$

and

$\int kf(x) dx = k \int f(x) dx.$

Additionally, the integral of the sum or difference of two or more functions is equal to the sum or difference of the integrals of each function:

$\int(f(x)\pm g(x))\, dx = \int f(x)\, dx \pm \int g(x) \, dx.$

So, for the function

$f(x)=\simplify[unitFactor,unitPower]{{a_1}*x^{b_1}+{a_2}*x^{b_2}+{a_3}*x^{b_3}},$

the integral is

$\begin{split}\simplify[unitFactor,unitPower]{int({a_1}*x^{b_1}+{a_2}*x^{b_2}+{a_3}*x^{b_3},x)} &\,= \simplify{{a_1}int(x^{b_1},x)+{a_2}int(x^{b_2},x)+{a_3}int(x^{b_3},x)} \\&\,= \simplify[all,fractionNumbers]{({a_1}*x^{b_1+1})/{b_1+1}+({a_2}*x^{b_2+1})/{b_2+1}+({a_3}*x^{b_3+1})/{b_3+1}}+c.\end{split}$

Note: You only need to put one $c$ term here, you do not need to put a separate constant term for each calculation.

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Christian Lawson-Perfect 2 years, 6 months ago

Ben McGovern 4 years ago

Ben McGovern 4 years, 8 months ago

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Integration: Using a Table of Integrals 2

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

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Comment

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Christian Lawson-Perfect 2 years, 6 months ago

Ben McGovern 4 years ago

Ben McGovern 4 years, 8 months ago

Error in variable testing condition

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Generated value: integer

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Gap-fill

Generated value: `integer`