Definite integration

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Ready to use

4 years ago

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Name	Status	Author	Last Modified
Definite integration	Ready to use	Martin Jones	24/03/2022 13:48
Basic integration 1	Ready to use	Martin Jones	14/07/2022 14:21
Integration	Ready to use	Shaheen Charlwood	27/10/2022 18:51

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Question statement

Integrate each of the following basic functions first indefinitely and then evaluate with the given limits.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	1
b	integer	4
c	integer	-2
d	integer	12
a1	number	22.0066984305
a2	number	44.0347488306
a3	number	-1.6890804934
a4	number	-1.6449511332
a5	number	-11.8400883159

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(a) and (b):

$\int_\var{d-2}^\var{d}\simplify[all]{{a}*x-sin({b}*x)}\,dx=\left[\simplify{{a}*x^2/2+cos({b}*x)/{b}}\right]_\var{d-2}^\var{d}=\var{a1}$

$\int_\var{d}^\var{d+3}\simplify[all]{{c}/x^{a+1}+{b}*sqrt(x)}\,dx=\left[\simplify{{-c/a}/x^{a}+{2*b/3}*x^(3/2)}\right]_\var{d}^\var{d+3}=\var{a2}$

(e) and (f):

$\int_{-2}^\var{a-2}\simplify[all]{{c+1}*exp(x/{b})-{a}}\,dx=\left[\simplify{{b*(c+1)}*exp(x/{b})-{a}*x}\right]_{-2}^\var{a-2}=\var{a3}$

(g) and (h):

$\int_\var{b}^\var{b+a}\simplify[all]{{c}/({b}*x)+{b}/{a+1}*cos({c}*x)}\,dx=\left[\simplify{{c}/{b}*ln(x)+{b}/{c*(a+1)}*sin({c}*x)}\right]_\var{b}^\var{b+a}=\var{a4}$

(i) and (j):

$\int_\var{a}^\var{a+1}\simplify[all]{x^{b-1}/{b+2}-{d}+{c}*exp({-a}*x)}\,dx=\left[\simplify{x^{b}/{b*(b+2)}-{d}*x-{c/a}*exp({-a}*x)}\right]_\var{a}^\var{a+1}=\var{a5}$

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Martin Jones 4 years ago

Martin Jones 4 years ago

Martin Jones 10 years, 2 months ago

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Generated value: `integer`

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Definite integration

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Martin Jones 4 years ago

Martin Jones 4 years ago

Martin Jones 10 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Mathematical expression

Advanced settings

Checking accuracy

Variable value generators

Pattern restriction

Variables

String restrictions

Generated value: `integer`