MX2 Integration Marathon 2021 (1 Viewer)

CM_Tutor

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At first, I thought you meant a much more difficult problem:

 

Qeru

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... that isnt the integral.

am i missing something? this doesn't look like a one line answer.
He basically defined that integral as a function similar to the error function or Si(x) etc.
 

idkkdi

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He basically defined that integral as a function similar to the error function or Si(x) etc.
what. it looks like he diffed the integral to get what's the integrand to me.
 

CM_Tutor

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Ok anyone want to try this (stumped me lol):

I don't see an obvious way to approach this. Integral calculator can't find an answer in elementary functions, which suggests that none of the common approaches will work. What makes you confident that there is an answer with the realm of MX2 possibilities?
 

Qeru

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I don't see an obvious way to approach this. Integral calculator can't find an answer in elementary functions, which suggests that none of the common approaches will work. What makes you confident that there is an answer with the realm of MX2 possibilities?
I found it on this other forum for Calc 1 (forgot where). Also I found this hint: https://math.stackexchange.com/ques...he-integral-of-sqrt-sin-sqrt-x-cos-sqrt-x-1x2

Not sure if that leads anywhere though
 

CM_Tutor

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This is much tougher than I first thought as you keep running into the exponential integral, (or a transform of it), being integrals such as



Transforms include the denominator being a linear function of or the numerator as . Properly, the exponential integral is defined (over the complex plane) as



and it cannot be expressed in elementary functions.

However, there is a closed form for this integral:




For those who want to try to solve the problem yourselves, you need to rewrite the integrand without creating terms of the form



where , , and , are constants and, in this case, or .

You will need something of the form:



where and are both of degree 1.



We know to leave alone as it is clearly a problem:


i.e. is a constant plus (or minus) the exponential integral.

 

s97127

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This is much tougher than I first thought as you keep running into the exponential integral, (or a transform of it), being integrals such as



Transforms include the denominator being a linear function of or the numerator as . Properly, the exponential integral is defined (over the complex plane) as



and it cannot be expressed in elementary functions.

However, there is a closed form for this integral:




For those who want to try to solve the problem yourselves, you need to rewrite the integrand without creating terms of the form



where , , and , are constants and, in this case, or .

You will need something of the form:



where and are both of degree 1.



We know to leave alone as it is clearly a problem:


i.e. is a constant plus (or minus) the exponential integral.

That's correct. what's the hardest integration problem that you have solved?
 

stupid_girl

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I know @vernburn has correctly split the interval. However, periodicity actually made the calculation easier rather than causing trouble.

Depending on how you express the antiderivative, the constant of integration may be different.
 

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