Integration: Using a Table of Integrals 3b

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Ben McGovern

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Christian Lawson-Perfect 2 years, 6 months ago

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Ben McGovern 3 years, 11 months ago

Gave some feedback: Ready to use

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Ben McGovern 4 years, 7 months ago

Created this as a copy of Integration: Using a Table of Integrals 3a.

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Question statement

Find the integral of $f(x)=\frac{\var{a}}{\var{b}x}$

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			Name	Type	Generated Value

			Name	Type	Generated Value

			a	integer	7
			b	integer	9

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random([1,2,3,5,7])

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Generated value: `integer`

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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

$f(x)= \frac{1}{x}$ has the integral

$\int \frac{1}{x} dx = \ln |x|+ c,$

and

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

So, for the function

$f(x)=\frac{\var{a}}{\var{b}x},$

the integral is

$\int \frac{\var{a}}{\var{b}x} dx \,= \simplify[unitFactor]{{a}/{b}int(1/x,x)} \,=\simplify[unitFactor]{{a}/{b} ln(abs(x)) +c}.$

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Christian Lawson-Perfect 2 years, 6 months ago

Ben McGovern 3 years, 11 months ago

Ben McGovern 4 years, 7 months ago

Error in variable testing condition

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Generated value: `integer`

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Integration: Using a Table of Integrals 3b

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 2 years, 6 months ago

Ben McGovern 3 years, 11 months ago

Ben McGovern 4 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`