Q. 9 - Calculus

Question

Preview of Differential Equations: 

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

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

Step-by-Step Solution

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