Question

Integrate the following functions: $\int \sin \left(mx\right)dx$

• A. $-\frac{\cos mx}{m}+c$
• B. $\frac{\cot mx}{4m}+c$
• C. $\frac{\sin 3mx}{m}+c$
• D. $-\frac{\cos 4mx}{4m}+c$

Answer 1

The correct option is A $-\frac{\cos mx}{m}+c$

$\int sin\left(mx\right)dx$

Let $mx=t$

$\frac{dt}{dx}=m$

$dx=\frac{dt}{m}$

Therefore

$\int sint\frac{dt}{m}$

$\frac{1}{m}\int sintdt$

$\frac{-cost}{m}+c$

$\frac{-cosmx}{m}+c$