Question

find the integral of sinxcosx using the identity sin(2x) = 2sinxcosx

Answer 1

\[\int\limits_{}^{}\sin x \cos x dx = \frac{1}{2}\int\limits_{}^{}\sin 2x dx\]

Answer 2

how did you know to use sin?
can you take me through step by step?

Answer 3

also you don't have to use that identity
let u=sinx
du=cosx dx
so we have
\[\int\limits_{}^{}u du=\frac{u^2}{2}+C=\frac{(sinx)^2}{2}+C\]

Answer 4

what do you mean how did you know to use sine? its says to in the problem
and also
sin(2x)=sin(x+x)=sinxcosx+sinxcosx=2sinxcosx

Answer 5

oh, i didn't know how to evaluate it in the problem like that

Answer 6

yes that way is simpler, but if you have to use that identity
then substitute sincos with 1/2 sin(2x) then use u substitution

Answer 7

do you know substitution yet?

Answer 8

yes....I completed the integration from your first answer dumbcow and i got the right answer. thanks everyone!

Answer 9

have fun
i love math too