Hi
I have to find the indefinite integral of:
f(t) = 6cos(3t)+5e^-10t
can anyone please show me step by step how to work this out.
many thanks
$\displaystyle \int f(t)~dt = 6 \int cos(3t)~dt + \int e^{-10t}~dt$
The first integral may be found by substituting $\displaystyle u = 3t \implies du = 3 dt$:
$\displaystyle \int cos(3t)~dt = \int cos(u) \cdot \frac{du}{3} = \frac{1}{3} \int cos(u)~du = \frac{1}{3} \cdot sin(u) = \frac{1}{3} \cdot sin(3t)$
For the second integral, use $\displaystyle u = -10t \implies du = -10 dt$.
You give this part a try. (And, of course, don't leave out that arbitrary constant at the end.)
-Dan