Question

integrate mod
(sin x-cosx ) 0 to p1/2

Answer 1

\[\int_o^{\pi/4} -(sin x - cos x)dx + \int_{\pi/4}^{\pi/2} (\sin x - \cos x)dx \]

Now you can do it.

Answer 2

We have
\[\int_0 ^{\pi/2} |\sin x - \cos x| dx\]
We know that from 0 to \(\pi/4\) sin x < cos x so
\[|\sin x - \cos x|= \cos x -\sin x\]
and from \(\pi/4\) to\(\pi/2\) sin x> cos x
so
\[|\sin x - \cos x|= \sin x -\cos x\]
We get
\[\int_0 ^{\pi/2} |\sin x - \cos x| dx=\int_0 ^{\pi/4} -(\sin x - \cos x) dx+\int_{\pi/4} ^{\pi/2} (\sin x - \cos x) dx\]
Can you do it now?

Answer 3

can you tel me the anwser

Answer 4

Just answer won't help you, Do you know how to integrate sin x and cos x?

Answer 5

Consider this your lucky day... the answer is \(2(\sqrt 2 - 1)\).