Class 12 Mathematics - Chapter Integrals NCERT Solutions | Integrals sin 2x
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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R = {(x, y): y = x + 5 and x < 4}
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R = {(x, y): y is divisible by x}
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R = {(x, y): x − y is as integer}
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