Question 1

Integrals sin 2x


The anti derivative of sin 2x is a function of x whose derivative is sin 2x.

It is known that,

\begin{align} \frac {d}{dx} (cos 2x) = 2 sin2x \end{align}

⇒ \begin{align} sin 2x =-\frac {1}{2} \frac {d}{dx}(cos 2x) \end{align} 

∴  \begin{align} sin 2x = \frac {d}{dx}\left(-\frac {1}{2}cos 2x\right) \end{align} 

Therefore, the anti derivative of sin2x is 

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

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