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NCERT Class XII Mathematics Chapter - - Solutions

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Exercise - 7.6
Integrate the functions in Exercises 134 to 155.
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Question : 135 of 271
Marks: +1, -0
xsin⁡3xx\sin 3x
Solution:  
Let I=∫xsin⁡3xdxI=\int x\sin 3x dx
=x(−cos⁡3x3)−∫ddxx(−cos⁡3x3)dx=x\left(-\frac{\cos 3x}{3}\right)-\int \frac{d}{dx}x\left(-\frac{\cos 3x}{3}\right)dx
=(−xcos⁡3x3)+13∫cos⁡3xdx= \left( -\frac{x\cos 3x}{3}\right)+\frac{1}{3}\int \cos 3x dx
=−xcos⁡3x3+13⋅sin⁡3x3+C=-\frac{x\cos 3x}{3}+\frac{1}{3}\cdot\frac{\sin 3x}{3}+C
=−13xcos⁡3x+19sin⁡3x+C=-\frac{1}{3}x\cos 3x+\frac{1}{9}\sin 3x+C
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