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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 : 134 of 271
Marks: +1, -0
xsin⁡xx\sin x
Solution:  
Let I=∫xsin⁡x dxI=\int x\sin x\,dx =x∫sin⁡x dx−∫[ddxx∫sin⁡x dx]dx=x\int\sin x\,dx-\int\left[\frac{d}{dx}x\int\sin x\,dx\right]dx
=x(−cos⁡x)−∫1(−cos⁡x)dx=x(-\cos x)-\int1(-\cos x)dx
=−xcos⁡x+∫cos⁡x dx=-x\cos x+\int\cos x\,dx
=−xcos⁡x+sin⁡x+C=-x\cos x+\sin x+C
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