Question

I am working on a question find the intrgral of sin(3πt)dt and my answer is -cos(3πt)+c but this seems to simple of an answer. am i m issing something?

Answer 1

you got the right answer

Answer 2

you forgot that you need to use a substitution. It's like the chain rule, later you will just do it in your head but for now write it out:\[\int\sin(3\pi t)\,dt\] set \(u=3\pi t\)
then \(du=3\pi dt\)
\[dt=\frac{du}{3\pi}\]plug those into the integral and you get \[\frac{1}{3\pi}\int\sin(u)\,du\]and now you can do that integral like you did initially, but don't forget to write your answer in terms of \(t\text{ instead of } u\).