Question 2

Integrals cos3x

Answer

The anti derivative of cos 3x is a function of x whose derivative is cos 3x.

It is known that,

\begin{align} \frac {d}{dx} (sin 3x) = 3 cos3x \end{align}

⇒ \begin{align} cos 3x =\frac {1}{3} \frac {d}{dx}(sin 3x) \end{align} 

∴  \begin{align} cos 3x = \frac {d}{dx}\left(\frac {1}{3}sin 3x\right) \end{align} 

Therefore, the anti derivative of cos3x is 

\begin{align} sin 2x \;is \frac {1}{3}sin 3x \end{align} 

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