## kylehberg 3 years ago what is the antiderivate of 9cos3t???

1. ParthKohli

integrate it

2. ParthKohli

In other words, what is $$9\cos3t$$ the derivative of?

3. ParthKohli

of course with respect to $$t$$.

4. Denebel

Hint: $\int\limits_{}^{} \cos ax dx = \frac{ \sin ax }{ a } + c$

5. ParthKohli

You start by taking the constant out.$9\int\cos (3t)$Use what Denebal gave.

6. ParthKohli

Denebel*

7. ParthKohli

By the way, you can also take $$u = 3t$$ :)

8. kylehberg

would it be sin3/2t^2

9. ParthKohli

Erm, no.

10. ParthKohli

$9\int \cos(3t)dt$Sorry for the mistake above

11. Chlorophyll

Where do you get 2t^2 ???

12. kylehberg

the antiderivate of 3t is 3/2t^2

13. ParthKohli

$9 \times{1 \over 3}\int \cos(u)du$$3\int \cos(u)du$$\implies 3\times \sin(u) + C$

14. Denebel

$9\int\limits_{}^{} \cos (3t) dt = \frac{ 9\sin(3t) }{ 3 } = 3\sin(3t) + C$

15. ParthKohli

Substituting $$u$$ back,$3\sin(3t) + C$Yep

16. kylehberg

thank you!... i can't do antiderivativs when they have a sin, cos, etc in them

17. Chlorophyll

∫ cosu dx = sinu / u' Does it make any sense to you?

18. Chlorophyll

or ∫cos ax dx = sin ax / a + C Does it make any sense at all?

19. kylehberg

yeah, thank you