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Integral of (cos(x))^2 in the hard way

Yankel

Active member
Jan 27, 2012
398
Hello guys

I am trying to solve the integral of cos(x) squared, i.e. (cos(x))^2, but not using the trigonometric identity of this function, but using integration by parts.

I tried turning it into 1*(cos(x))^2, but I didn't go too far, maybe did something wrong.

Am I on the right direction ?

cheers
 

Opalg

MHB Oldtimer
Staff member
Feb 7, 2012
2,704
Hello guys

I am trying to solve the integral of cos(x) squared, i.e. (cos(x))^2, but not using the trigonometric identity of this function, but using integration by parts.

I tried turning it into 1*(cos(x))^2, but I didn't go too far, maybe did something wrong.

Am I on the right direction ?
You would do better to write it as cos(x)*cos(x). After integrating by parts, use the fact that sin^2 = 1 – cos^2.
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
If I were going to tackle this using IBP, I would let:

\(\displaystyle u=\cos(x)\,\therefore\,du=-\sin(x)\,dx\)

\(\displaystyle dv=\cos(x)\,dx\,\therefore\,v=\sin(x)\)

What do you find?