Question

Preview of Differential Equations:

Given each of the following equations involving a functionf, find a possible formula for f(x).

$f\text{'}\left(t\right)=\sin bt$

Short answer

The possible formula for the function $f\text{'}\left(t\right)=\sin bt$is $f\left(t\right)=-\frac{1}{b}\cos bt$.

Step-by-step solution

Step 1. Given Information.

The function:

$f\text{'}\left(t\right)=\sin bt$

Step 2. Consider the function.

Consider the function,

$$\begin{gathered} f\left(t\right)=-\frac{1}{b}\cos bt \\ f\text{'}\left(t\right)=\frac{d}{dt}(-\frac{1}{b}\cos bt) \\ =-\frac{1}{b}(-\sin bt).b \\ =\sin bt \end{gathered}$$

So the function is$f\left(t\right)=-\frac{1}{b}\cos bt$