Solving Integral of cosX^2: Tips and Advice

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Homework Help Overview

The discussion revolves around the integral of cos(x^2) and the challenges associated with solving it. Participants explore various methods and express uncertainty about the feasibility of finding a solution using standard techniques.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss attempts at integration by parts and the half-angle formula, questioning their applicability to the integral of cos(x^2). There are inquiries about the inability to return to the original integral after differentiation.

Discussion Status

The conversation includes various attempts to clarify the problem, with some participants suggesting that certain methods may not apply. There is a recognition of the complexity of the integral, and while some guidance has been offered, there remains a lack of consensus on the approach to take.

Contextual Notes

Participants mention the need for concrete mathematical proofs regarding the impossibility of solving the integral using ordinary methods, indicating a desire for deeper understanding amidst the homework constraints.

evra
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i want someone to help me with the integral of cosX^2



i attempted using integrals by parts.. wat i got when i differentiate it i didn't go back to the same integral equation.
is it that it is not possible??
 
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evra said:
i want someone to help me with the integral of cosX^2

I'm not sure what you mean here. If you want to take the integral of \cos x^2, then this cannot be solved through ordinary methods. However, if you want to solve (cosx)^2, just apply the half-angle formula.
 
Last edited:
hi evra! :smile:
evra said:
i attempted using integrals by parts.. wat i got when i differentiate it i didn't go back to the same integral equation.
is it that it is not possible??

∫ cosx.cosx dx

= [sinx.cosx] + ∫sinx.sinx dx

= [sinx.cosx] + ∫ 1 dx - ∫cosx.cosx dx​

so 2∫ cosx.cosx dx = [sinx.cosx] + ∫ 1 dx :wink:

(or just use one of the standard trignonometric identites as gb7nash :smile: says)
 


mr gb7nash, yes i mean ∫cos x^2. but the relation u used above can't work. i tried it but the rsult i got when i defferentiate it i can't come back to the original answer.
please check it.
 
evra said:
i tried it but the rsult i got when i defferentiate it i can't come back to the original answer.
please check it.

nooo … you show us what you got :wink:
 


i got sinX^2 and when I differentiate this I got 2XcosX^2
 
evra said:
i got sinX^2 and when I differentiate this I got 2XcosX^2

(try using the X2 icon just above the Reply box :wink:)

no, if you want to find ∫ cos(x2) dx, then as gb7nash said, this cannot be solved through ordinary methods …

integration by parts, or the half-angle formula, will only work for ∫ cos2x dx :wink:
 


then its not possible... thanks! its like sinX^2.
BUT why is it that its not possible.. what are the prooves? a younger brother is bordering me with it and he said i should give him concret mathematical proves.
thanks
 


evra said:
then its not possible... thanks! its like sinX^2.
BUT why is it that its not possible.. what are the prooves? a younger brother is bordering me with it and he said i should give him concret mathematical proves.
thanks

It's possible with an infinite series expansion of sin(A), A=x^2
 
  • #10


no i don't think so because i did that and if i defferentiate the answer i got, i can't get back to sin(x2)
 

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