Question

Find an antiderivative of f(x)=4. assume that the value of the arbitrary constant is 0

Answer 1

`f(x)=4x`

Step-by-step explanation: According to the power rule of taking a derivative, if we have a certain function:

`f(x)=Cx^n+K`

Then the derivative of the f(x) would be as follows:

`\begin{gathered} (df(x))/(dx)=(d(Cx^n))/(dx)+(d(K))/(dx)=(d(Cx^n))/(dx)+0 \\ \text{ Implies }\Rightarrow(d(K))/(dx)=0 \\ \therefore\Rightarrow \\ (df(x))/(dx)=(d(Cx^n))/(dx)=C\cdot nx^((n-1)) \end{gathered}`

Using this rule in reverse we can calculate the antiderivative of the provided f(x) as follows:

`\begin{gathered} (dF(x))/(dx)=(d(Cx^n))/(dx)+(d(K))/(dx)=f(x)=4 \\ K=0 \\ \therefore\Rightarrow \\ (dF(x))/(dx)=(d(Cx^n))/(dx)=4\Rightarrow4x\Rightarrow C=4 \\ \text{ }\therefore\rightarrow \\ f(x)=4x \\ \\ \end{gathered}`