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NCERT Class XII Mathematics Chapter - - Solutions

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Exercise - 7.3
Find the integrals of the functions in Exercises 62 to 83.
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Question : 63 of 271
Marks: +1, -0
sin⁡3xcos⁡4x\sin 3x \cos 4x
Solution:  
Let I=∫sin⁡3xcos⁡4xdxI=\int \sin 3x \cos 4x dx =12∫[sin⁡(3x+4x)+sin⁡(3x−4x)]dx=\frac{1}{2}\int \left[ \sin(3x+4x)+\sin(3x-4x) \right] dx
=12∫(sin⁡7x−sin⁡x)dx=\frac{1}{2}\int (\sin 7x - \sin x) dx =12(−cos⁡7x7)−12(−cos⁡x)+C=\frac{1}{2}\left( \frac{-\cos 7x}{7} \right) - \frac{1}{2}(-\cos x) + C =−114cos⁡7x+12cos⁡x+C=-\frac{1}{14}\cos 7x + \frac{1}{2}\cos x + C
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