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NCERT Class XII Mathematics Chapter - - Solutions

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Exercise - 7.2
Integrate the functions in Exercises 23 to 59.
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Question : 49 of 271
Marks: +1, -0
sin⁡2xcos⁡2x\sqrt{\sin 2x}\cos 2x
Solution:  
Let I=sin⁡2xcos⁡2xdxI=\sqrt{\sin 2x}\cos 2x dx
Put sin⁡2x=t⇒2cos⁡2xdx=dt\sin 2x = t \Rightarrow 2\cos 2x dx = dt
∴I=12∫t1/2dt\therefore I = \frac{1}{2} \int t^{1/2} dt =12⋅t1/2+11/2+1+C= \frac{1}{2} \cdot \frac{t^{1/2+1}}{1/2+1} + C
=12×23t3/2+C= \frac{1}{2} \times \frac{2}{3} t^{3/2} + C =13(sin⁡2x)3/2+C= \frac{1}{3} (\sin 2x)^{3/2} + C
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