2}}\textrm dx$

Asked Nov 06 '21 at 15:03

Active Sep 13 '22 at 16:48

Viewed 246 times

$$\int_0^{\pi/2} e^{-x} \frac{(\sin x)^{1/2}}{(\sin x)^{1/2} + (\cos x)^{1/2}}\textrm dx$$

I can't seem to solve this integral, I have tried integration by parts as well as some substitutions. Please help, a hint would be better appreciated. P.S. This is my first time posting question in coded format, sorry if it's wrong.

edited Nov 06 '21 at 15:12

poyea

1,662

asked Nov 06 '21 at 15:03

Confused_nerd

2

Are you sure that there is a simple answer? – José Carlos Santos Nov 06 '21 at 15:29
@JoséCarlosSantos Yes, I am – Confused_nerd Nov 06 '21 at 15:37
And do you happen to know what that simple answer is? – José Carlos Santos Nov 06 '21 at 16:25
@JoséCarlosSantos Yes, 0.339727. I found this using wolfram alpha. This question was given to a friend of mine by his teacher, who too has been unable to solve this. – Confused_nerd Nov 06 '21 at 16:30
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@Confused_nerd, I wonder how did you conclude that integral has a simple answer. Note that merely convergence doesn't mean that answer is simple. – RAHUL Nov 06 '21 at 16:38
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By that argument, whenever an integral converges to something, it is simple. – José Carlos Santos Nov 06 '21 at 16:39
@RAHUL I am not sure what you mean "simple", isn't an answer to a finite integral a simple real number?? Sorry, but if there are "complex" answers, then I am not aware of them. – Confused_nerd Nov 06 '21 at 16:41
@José Carlos Santos, Sir I believe that merely convergence doesn't suffice that integral is simple(My argument is that, it depends on anti-derivative of the integral). Sir, for instance have a look at this,https://math.stackexchange.com/questions/4293416/evaluate-i-alpha-int-0-infty-frac-arctan-left-alpha-x-operatorn. It converges but not simple – RAHUL Nov 06 '21 at 16:43
@Confused_nerd, Honestly speaking I don't know how answer looks like and how complicated it is. But it just seems to me that it's difficult. That's it. – RAHUL Nov 06 '21 at 16:44
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This seems hopeless and mostly a waste of time, not sure why would a teacher give this. See also this (unanswered for quite a few years). – Zacky Nov 06 '21 at 18:55
@Zacky This is literally the same question. Just one substitution away. – Laxmi Narayan Bhandari Nov 06 '21 at 19:02
@LaxmiNarayanBhandari Yes, but it can't be marked as a duplicate since that has no answers. – Zacky Nov 06 '21 at 19:02
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@Zacky That's the main problem. Is there any way to merge two different posts? – Laxmi Narayan Bhandari Nov 06 '21 at 19:03
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@Zacky Thanks for the link to other question, I will not waster any more time on this. – Confused_nerd Nov 07 '21 at 04:23
@Confused_nerd definitely the right choice. – Laxmi Narayan Bhandari Nov 07 '21 at 04:36
Has anyone tried this with a square contour? – Max0815 Sep 13 '22 at 22:27

Integral $\int_0^{\pi/2} e^{-x} \frac{(\sin x)^{1/2}}{(\sin x)^{1/2} + (\cos x)^{1/2}}\textrm dx$

0 Answers0