MX2 Integration Marathon (1 Viewer)

stupid_girl

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This one should be harder.
I think I've masked the underlying substitution quite well.:cool:
 

Paradoxica

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Anyone has guessed the substitution?
I can reduce it but I can't evaluate it. Are you sure this integral is expressible in terms of elementary functions?

The numerical integration returns 0.4690815321272337326612091235046416327076, which has no simple form in the Inverse Symbolic Calculator.
 

Paradoxica

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Once the substitution is uncovered, it is not much fun.

tried this as my initial thought (i knew getting rid of the denominator was a necessary step), didn't get very far for some reason, maybe i made an arithmetical error somewhere
 

stupid_girl

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a new one...shouldn't be too hard:p
Feel free to share your attempt.

Find the area bounded by x-axis and the curve
.
 

Nav123

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a new one...shouldn't be too hard:p
Feel free to share your attempt.

Find the area bounded by x-axis and the curve
.
Not sure if this is still active but I'll give this a go for fun (let me know if I've made any mistakes or there is an easier way). The x-ints are
Using the corrected identity (Thanks to vernburn for showing that there is a factor of a half):

where E is an even function and O is an odd function. The integral simplifies:







Let and
where




where

So
 
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stupid_girl

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Your approach is correct but unfortunately a factor of 1/2 is missing somewhere.
 

Qeru

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another one

Feel free to share your attempt.
Using the identity:









For the second integral, let





and which can be found quite easily using two applications of integration by parts . Now using IBP on the main integral: hence



using the previous results







Using the fact that sine is odd and cosine is even.

Now for the first integral letting gives identical bounds hence

So in total:

Wow that was a long one, unfortunately didn't get it out as I'm off by a bit, can anyone see my error?
 

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