Different answers when I do the same integration

Hey,

I'm getting different answers when I perform the same integration but by just expanding the squared term.

How is this possible?

As I procced further, I'm getting 2 completely different answers as my result.

Which one is correct?

PS: I'm getting the same answer even after using 'IgnoreAnalyticConstraints',true.

Thanks

[Stephen23]

They don't look very similar:

X = linspace(0,pi,1e3);
Y1 = (1-cos(X)).^2;
Y2 = 1+cos(X).^2-2*(1-cos(X));
plot(X,Y1,X,Y2)

[Nishanth Pradyumna]

@Stephen23

I have just used the identity (a-b)^2 = (a^2 + b^2 - 2ab). Technically, I should get the same results.

[David Hill]

-2ab = -2*cos(n) and is not the same as -2*(1-cos(x))

[Nishanth Pradyumna]

@David Hill

My bad. That was a dumb typo. Thanks.

Answer 1

[David Hill]

They are not the same expressions.

syms x
int((1+cos(x))^2,0,pi)

ans = 

int(1+2*cos(x)+cos(x)^2,0,pi)

ans = 

int(1+cos(x)^2-2*(1-cos(x)),0,pi)%this is not the same expression

ans = 

[Nishanth Pradyumna]

My bad, added the wrong screenshot. please try int((1-cos(x))^2,0,pi).

I did not get the same answer with that. (please check the updated screenshot)

[Torsten]

Look up the binomial formula:

(a-b)^2 = a^2 - 2*a*b + b^2