Question

Fun Integral:

Answer 1

\[\int\limits_{}^{}\sqrt{1+\sin 2x } dx\]

Answer 2

\[\sqrt{\color{red}{1}+\sin (2x)} \\~\\=\sqrt{\color{red}{\sin^2x+\cos^2x}+\sin (2x)} \\~\\=\sqrt{(\sin x + \cos x)^2} \\~\\= |\sin x +\cos x|\]

Answer 3

dang have you seen this before?

Answer 4

I guess several time haha
but what can be done with that absolute value ?

Answer 5

that absolute value is just like when you want to integrate the absolute value of x, you separate into the integral of x for all numbers equal or greater than 0 and the integral of -x for all numbers equal or less than 0