Question

find the anti derivative of \[\sin \pi x-2\cos \frac{ x }{ 2 }\]

Answer 1

integrate it

Answer 2

well for the first part i got \[-\frac{ \cos \pi x }{ \pi} \] I believe that's correct. but I'm having trouble with the second half

Answer 3

would I use constant multiple rule and then just integrate cosine?

Answer 4

+4sin(x/2)

Answer 5

no minus sorry

Answer 6

To avoid any confusion , go for x/2 = t... then convert dx into dt...

Answer 7

Oh I see how it's done now. so you just did \[-2(\frac{ 1 }{ \frac{ 1 }{ 2 } })\sin \frac{ x }{ 2 } \] correct?

Answer 8

and you got -4sinx/2 correct?

Answer 9

yes

Answer 10

Yeah, that's like divide the {multiplied of 'x'} and do not change anything for 'added or subtracted'...
Like if there's cos(ax+ b)... then divide the (multiplied) a... and do not make changes for 'b' after integrating the cos term...