Question

Prove$$\begin{gathered} \mathrm{The}\mathrm{objective}\mathrm{is}\mathrm{to}\mathrm{prove}\mathrm{that}\int kf\left(x\right)dx=k\int f\left(x\right)dxinwords. \\ \mathrm{Let}\mathrm{Fx}\mathrm{be}\mathrm{the}\mathrm{derivative}\mathrm{of}f\left(x\right). \end{gathered}$$

Short answer

Proved

Step-by-step solution

Step 1. To prove

$\int kf\left(x\right)dx=k\int f\left(x\right)dx$

Step 2. Proving

$$\begin{gathered} \int kf\left(x\right)dx=k\int f\left(x\right)dx \\ =\int kf\left(x\right)dx \\ =k{F}^{\text{'}}\left(x\right)+C \\ =k\left(F^{\text{'}}\left(x\right)+\frac{C}{k}\right) \\ =\int kf\left(x\right)dx \\ \mathrm{Hence}\mathrm{Proved} \end{gathered}$$]