Quick integration question

Why is the integral of cos(2x) = sin(x)cos(x)?

Why wouldn't the integral of cos(2x) = sin(2x)/2 ?

If you take the derivative of sin(2x) / 2 you use chain rule and get cos(2x) so wouldn't the fundamental theorem of calculus tell you that therefore the integral of cos(2x) = sin(2x)/2?

Question

Quick integration question

Why is the integral of cos(2x) = sin(x)cos(x)?

Why wouldn't the integral of cos(2x) = sin(2x)/2 ?

If you take the derivative of sin(2x) / 2 you use chain rule and get cos(2x) so wouldn't the fundamental theorem of calculus tell you that therefore the integral of cos(2x) = sin(2x)/2?

amistre64 · Answer

you do know your trig identities right?

anonymous · Answer

yeah

amistre64 · Answer

you say yeah, but your question belies you

anonymous · Answer

Hmm I'm guessing what you're saying is that sin(x)cos(x) = sin(2x)/2

amistre64 · Answer

sin(2x)/2  is fine for an answer ... but it has an equaivalent identity

amistre64 · Answer

yep

amistre64 · Answer

sin(2x)/2 = 2sinx cosx/2

anonymous · Answer

Oh okay. I was confused cause I'm doing homework online (integration by parts) and it said my answer was wrong. So I guess they want it in the form of sinxcosx even though it's the same thing as sin(2x)/2

amistre64 · Answer

yeah, i loathe online homework 'solutions'

anonymous · Answer

Ha yeah, well thanks for the help.

amistre64 · Answer

youre welcome