Question

How can I prove that
que ∫sen(kx) = (-cos(kx))/k+C

in details!!

Answer 1

Your question is to prove
\[\int \sin (kx) dx= -\frac{\cos kx}{k}+c\]???

Answer 2

Yes

Answer 3

Do you know this?
\[\int \sin x=-\cos x +c\]

Answer 4

yes

Answer 5

Our integral is
\[\int \sin kx\ dx\]
Let's substitute kx=u so
\[kdx=du\]
or
\[dx=\frac{du}{k}\]
Our integral changes now to
\[\int \sin (u) \frac{du}{k}\]
k is constant so it'll come out of the integral
\[\frac{1}{k}\int \sin (u) \du\]
Now it's easy, integrating we get
\[-\frac{\cos u}{k}+c\]
put u =kx
We get
\[-\frac{\cos kx}{k}+c\]

Answer 6

THANK YOU!!!!

Answer 7

Welcome:D