Question

Can somebody walk me through writing the antiderivative equation of -cos(x/11)+15?

Answer 1

Solving or just writing the equation?

Answer 2

\[\int\limits_{}^{}-\cos(\frac{ x }{ 11 })+15dx \]

Answer 3

I know nothing about circuits @alfers101 sorry.

Answer 4

oh :( do you know someone? @Psymon

Answer 5

@Psymon Just writing.

Answer 6

Alrighty, gotcha :3

Answer 7

Well, wecan start by treating this as two integrals:
\[-\int\limits_{}^{}\cos(\frac{ x }{ 11 })dx+\int\limits_{}^{}15dx \]Now:
\[\int\limits_{}^{}\cos(u)=\sin(u)+C\]That is the straightforward integration for cosine to sine, but we also have to worry about the dx. We must solve for dx when we do integrals. This is done with u-substitution. Notice how I put cos(u), sin(u). Well, that is exactly what we do, we say something like:
Let u = x/11
Now dx means derivative of x. So to solve for dx, we must take the derivative of our u = x/11. If I take the derivative, I get:
\[du=\frac{ dx }{ 11 }\]
\[dx=11du \]Now I can substitute this for dx in our integral. This means we have:
\[-11\int\limits_{}^{}\cos(u)du=-11\sin(u)=-11\sin(\frac{ x }{ 11 })\]
All I did was factor out the 11 to the outside of the integral. This is perfectly fine to do. Now the second integral is simply:
\[\int\limits_{}^{}15dx \]Now because we only have a number, there is no real x to solve for dx. So now we just follow the regular integration formula which is:
\[\int\limits_{}^{}x ^{n}=\frac{ x ^{n+1} }{ n+1 }\]
In this case, we have an x^0 power, because there is no x. This means all we do to integrate 15 is add an x. So in total, our whole integral is:
\[-11\sin(\frac{ x }{ 11 })+15x+C \]Just don't forget the plus C> We that plus C there to account for the fact that the original function whose derivative is -cos(x/11) + 15 MAY have had a constant that we are unaware of. So this would be your entire answer for your integral problem : )

Answer 8

sugoi! :O @Psymon

Answer 9

ありがとう :3