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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 : 68 of 271
Marks: +1, -0
sin⁡4xsin⁡8x\sin 4x \sin 8x
Solution:  
Let I=∫sin⁡4xsin⁡8xdxI=\int \sin 4x \sin 8x dx
=12∫2sin⁡4xsin⁡8xdx=\frac{1}{2}\int 2\sin 4x \sin 8x dx
=12∫(cos⁡4x−cos⁡12x)dx    [∵2sin⁡Asin⁡B=cos⁡(A−B)−cos⁡(A+B)]=\frac{1}{2}\int (\cos 4x - \cos 12x) dx \; \; [\because 2\sin A \sin B = \cos(A-B) - \cos(A+B)]
=12[14sin⁡4x−112sin⁡12x]+C=\frac{1}{2}\left[\frac{1}{4}\sin 4x - \frac{1}{12}\sin 12x\right]+C
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