Question

finding the derivative (check my work)

Answer 1

a(t) = 3cos t -2 sin t
Im finding the antiderivative
should i be getting
v(t) = 3sin t + 2 cos t + c
OR
v(t) = 3 sin t - 2 cos t + C

because the antideriv of sin is - cos, but we already have a neg there

Answer 2

first one...

Answer 3

The negative sign coming from the antiderivative will cancel with the negative sign initially there.
So:
- 2 sin t goes to - 2 (-cos t) = + 2 cos t

Answer 4

v(t) = 3sin t + 2 cos t + c is right

Answer 5

The negative in -2sin(t) gets multiplied with the negative that arises when you integrate sin(t), hence giving you a positive +2cos(t). So V(t) = 3sin(t) + 2cos(t) + C is correct.