Double integral,

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Newcastle University Mathematics and Statistics

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Newcastle University Mathematics and Statistics 9 years, 2 months ago

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Question statement

Evaluate the following repeated integral:

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			Name	Type	Generated Value

a	integer	7
upper	number	2980.9579870417
lower	number	1096.6331584285
m	integer	2
t	integer	3
ans	number	1884.325
fun	string	$\exp(x^{\var{m}}+\var{a})$

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

$I=\;$ Unnamed gap

Input your answer to 3 decimal places.

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We want to find

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

The innermost integral gives:

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

So we have to find $\displaystyle I=\int_0^1\simplify[all]{{m}x^{m-1}}$ {fun} $dx$

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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Taxonomy: mathcentre

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Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

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Generated value: `integer`

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Double integral,

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`