Ugur's copy of Resolve a double integral

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Ugur Efem

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2 years ago

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Ugur Efem 2 years ago

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Ugur Efem 2 years ago

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Ugur Efem 2 years, 1 month ago

Created this as a copy of Resolve a double integral.

Name	Status	Author	Last Modified
Resolve a double integral	Ready to use	Christian Lawson-Perfect	20/11/2019 14:51
Luis's copy of Resolve a double integral	draft	Luis Hernandez	30/11/2018 01:11
Luis's copy of Resolve a double integral	draft	Luis Hernandez	30/11/2018 14:58
Ugur's copy of Resolve a double integral	Ready to use	Ugur Efem	04/04/2023 15:34

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Question statement

Evaluate the following repeated integral:

$I = \int_0^1 \; \int_0^{\simplify[all]{x^{m-1}}}\var{m} \var{fun} \; \mathrm{d}y\; \mathrm{d}x$

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	8
upper	number	0.4121184852
lower	number	0.9893582466
m	integer	3
t	integer	2
ans	number	-0.577
fun	string	\cos(x^{3}+8)

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Generated value: `integer`

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We want to find

$I=\int_0^1 \; \int_0^{\simplify[all]{x^{m-1}}} \var{m} \var{fun} \; \mathrm{d}y \; dx$

The innermost integral gives:

$\int_0^{\simplify[all]{x^{m-1}}}\var{m} \var{fun} \; \mathrm{d}y = \left[\var{m}y \; \var{fun} \right]_0^{\simplify[all]{x^{m-1}}}=\simplify[all]{{m}x^{m-1}} \var{fun}$

So we have to find $\displaystyle I=\int_0^1\simplify[all]{{m}x^{m-1}} \var{fun} \; \mathrm{d}x$ .

Note that if we use the substitution $u=\simplify[all]{x^{m}+{a}}$ then it is easy to find this last definite integral and we find that:

$I=\var{ans}$ to 3 decimal places.

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This question is used in the following exams:

Double Integrals by Ugur Efem in Ugur's workspace.
MATH2901 - Repeated Integrals by Blathnaid Sheridan in Blathnaid's workspace.
MATH2901_CA2 by Blathnaid Sheridan in Blathnaid's workspace.

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Ugur Efem 2 years ago

Ugur Efem 2 years ago

Ugur Efem 2 years, 1 month ago

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Ugur's copy of Resolve a double integral

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Ugur Efem 2 years ago

Ugur Efem 2 years ago

Ugur Efem 2 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`