Integration (Negative and Fractional Powers) 3

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Christian Lawson-Perfect 2 years, 7 months ago

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Ben McGovern 4 years, 8 months ago

Created this as a copy of Integration: Using a Table of Integrals 4.

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
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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
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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
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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
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Question statement

Using the Table of Integrals/Antiderivatives, calculate the integral of $f(x)=\var{a}e^{\simplify[fractionNumbers]{{b}x}}$

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

$f(x)= e^{mx}$ has the integral

$\int e^{mx} dx = \frac{1}{m}e^{mx}+c,$

and

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

So, for the function

$f(x)=\simplify[fractionNumbers]{{a}e^({b}x)},$

the integral is

$\begin{split} \int\simplify[fractionNumbers]{{a}e^({b}x)} dx \,= \simplify[unitFactor,fractionNumbers]{{a}int(e^({b}x),x)} &\,=\var{a}\times\simplify[unitFactor,fractionNumbers,unitDenominator]{(e^({b}x)/{b})} +c, \\ &\,=\simplify[unitFactor,fractionNumbers]{{a/b} e^({b}x)+c}. \end{split}$

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This question is used in the following exams:

Integration Basic by Jinhua Mathias in Maths 3-2020.
Summer Quiz 4 by Kate Vincent in Kate's workspace.
Quiz 4 by Kate Vincent in Kate's workspace.

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Integration (Negative and Fractional Powers) 3

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Christian Lawson-Perfect 2 years, 7 months ago

Ben McGovern 4 years ago

Ben McGovern 4 years, 8 months ago

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Integration (Negative and Fractional Powers) 3

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

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Comment

Checkpoint description

Christian Lawson-Perfect 2 years, 7 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`