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Problem:\int_{0}^{1}[arcsin [2-x]]-[arcsin [x]] dx
- Thread starter Seimuna
- Start date
D
Deleted member 4993
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Seimuna said:erm...then how to rewrite it into double integral ? & how to switch the order of integration ?
This is an integral of summation functions with single variable - where is double integral coming from?
Subhotosh Khan said:This is an integral of summation functions with single variable - where is double integral coming from?
that is the point...i thot im the only 1 thought of this... but this is the question given... i don think the question is wrong... so, i think, i am the 1 who dono how to change it to double integral and rewrite it...
D
Deleted member 4993
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What did the question "exactly" ask?
D
Deleted member 4993
Guest
Seimuna said:Evaluate \(\displaystyle \int_{0}^{1} [arcsin [2-x]]-[arcsin [x]] dx\) by rewriting it as double integral and switching the order of integration.
This does not make sense at all!!
arcsin(2-x) is not defined for x<1 and your integration limit is 0 to 1
D
Deleted member 4993
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The problem would make sense - if the statement was:
Now it would be area contained between two lines and can be converted to double integral.
Take it back - as Cody pointed out below arcsin(2x) is undefined for x > (1/2).
Shoud have taken my own advice - should have plotted the functions first ......
The new improved function that would make sense:
Seimuna said:Evaluate \(\displaystyle \int_{0}^{1} [arcsin [2*x]]-[arcsin [x]] dx\) by rewriting it as double integral and switching the order of integration.
Now it would be area contained between two lines and can be converted to double integral.
Take it back - as Cody pointed out below arcsin(2x) is undefined for x > (1/2).
Shoud have taken my own advice - should have plotted the functions first ......
The new improved function that would make sense:
Seimuna said:Evaluate \(\displaystyle \int_{0}^{1} [arcsin [2*x \, - \, 1]]-[arcsin [x]] dx\) by rewriting it as double integral and switching the order of integration.
Subhotosh Khan said:The problem would make sense - if the statement was:
Seimuna said:Evaluate \(\displaystyle \int_{0}^{1} [arcsin [2*x]]-[arcsin [x]] dx\) by rewriting it as double integral and switching the order of integration.
Now it would be area contained between two lines and can be converted to double integral.
if is in this case, how shud i convert it ?
D
Deleted member 4993
Guest
You should plot the functions first - get a graphical understanding of the domain and range of the functions, as it relates to the problem.
D
Deleted member 4993
Guest
[/quote]Seimuna said:Evaluate \(\displaystyle \int_{0}^{1} [arcsin [2*x \, - \, 1]]-[arcsin [x]] dx\) by rewriting it as double integral and switching the order of integration.
\(\displaystyle \int_{0}^{1} [arcsin [2*x \, - \, 1]]-[arcsin [x]] dx\)
\(\displaystyle =\int_{0}^{1} \int^{arcsin [2*x \, - \, 1]}_{arcsin [x]} dy \, dx\)