Integrating cos²x with integration by parts

[evra]

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??

 

[gb7nash]

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.

 

[tiny-tim]

hi evra!

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

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

 

[evra]

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.

 

[tiny-tim]

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

 

[evra]

i got sinX^2 and when I differentiate this I got 2XcosX^2

 

[tiny-tim]

i got sinX^2 and when I differentiate this I got 2XcosX^2

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

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

 

[evra]

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

 

[Apphysicist]

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

 

[evra]

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)