CB4 Definite integration

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Lauren Desoysa	said	Ready to use	1 year, 1 month ago
Andrew Neate	said	Needs to be tested	1 year, 1 month ago

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Will Morgan 11 months, 2 weeks ago

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Lauren Desoysa 1 year, 1 month ago

Gave some feedback: Ready to use

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Andrew Neate 1 year, 1 month ago

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Andrew Neate 1 year, 1 month ago

Created this as a copy of Integration: Definite Integrals 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	09/04/2024 15:44
CD3 Integration - Substitution	Ready to use	Andrew Neate	09/04/2024 15:56
CB4 Definite integration	Ready to use	Andrew Neate	09/04/2024 15:45
CB6 Differentiating Trig 1	Ready to use	Andrew Neate	09/04/2024 15:46
CB7 Differentiating Trig 2	Ready to use	Andrew Neate	09/04/2024 15:46
CB8 Differentiating with Trig 3	Ready to use	Andrew Neate	09/04/2024 15:52
CB9 Differentiating with Exponentials	Ready to use	Andrew Neate	09/04/2024 15:52
CB10 Differentiation with logs	Ready to use	Andrew Neate	09/04/2024 15:43
CB3 - Indefinite integration - polynomials	Ready to use	Andrew Neate	09/04/2024 15:45
CB5 - Finding turning points	Ready to use	Andrew Neate	09/04/2024 15:46

There are 150 other versions that do you not have access to.

Question statement

Evaluate

$\int_{\var{n_1}}^{\var{n_2}}\simplify[unitFactor, unitPower, fractionNumbers]{{a_1}*x^{b_1}+{a_2}*x^{b_2}+{a_3}*x^{b_3}} \,dx.$

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			Name	Type	Generated Value

			Name	Type	Generated Value

a_1	integer	4
a_2	integer	5
a_3	integer	4
b_1	integer	3
b_2	integer	2
b_3	integer	1
n_1	integer	0
n_2	integer	4
eval2	number	394.6666666667
eval1	number	0
eval2a	number	394.667
eval1a	number	0.000
sol	number	394.6666666667
sol1	number	394.67

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Generated value: `integer`

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eval1
eval2

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1. Gap Gap 0 Mathematical expression
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Advice

Integrating a function of the form

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

$\int_a^b x^n dx = \left[\frac{x^{n+1}}{n+1}\right]_a^b,$

and

$\int_a^b kf(x) dx = k \int_a^b f(x) dx.$

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:

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

Therefore,

$\begin{split}\simplify[unitFactor,unitPower]{defint({a_1}*x^{b_1}+{a_2}*x^{b_2}+{a_3}*x^{b_3},x,{n_1},{n_2})} &\,= \simplify{{a_1}defint(x^{b_1},x,{n_1},{n_2})+{a_2}defint(x^{b_2},x,{n_1},{n_2})+{a_3}defint(x^{b_3},x,{n_1},{n_2})} \\ &\,= \left[\simplify[all,fractionNumbers]{{a_1}x^{b_1+1}/{b_1+1}+{a_2}x^{b_2+1}/{b_2+1}+{a_3}x^{b_3+1}/{b_3+1}}\right]_\var{n_1}^\var{n_2} \\ &\,= \left[\simplify[all,fractionNumbers,!collectNumbers]{{a_1*n_2^(b_1+1)}/{b_1+1}+{a_2*n_2^(b_2+1)}/{b_2+1}+{a_3*n_2^(b_3+1)}/{b_3+1}}\right] -\left[\simplify[all,fractionNumbers,!collectNumbers]{{a_1*n_1^(b_1+1)}/{b_1+1}+{a_2*n_1^(b_2+1)}/{b_2+1}+{a_3*n_1^(b_3+1)}/{b_3+1}}\right] \\ &\,= \simplify[!collectNumbers]{{eval2a}-{eval1a}} \\ &\,=\var{sol1} \end{split}$

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Will Morgan 11 months, 2 weeks ago

Lauren Desoysa 1 year, 1 month ago

Andrew Neate 1 year, 1 month ago

Andrew Neate 1 year, 1 month ago

Error in variable testing condition

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Generated value: `integer`

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CB4 Definite integration

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Will Morgan 11 months, 2 weeks ago

Lauren Desoysa 1 year, 1 month ago

Andrew Neate 1 year, 1 month ago

Andrew Neate 1 year, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`