Gujarat BoardEnglish MediumSTD 12 ScienceMathsINTEGRALS2 Marks
Question
Integrate the function in exercise.
$\text{x} \ \sin\text{x}$
✓
Answer
Let $\text{I}=\int\text{x}\sin\text{x dx}$
Taking x as first function and x as second function and integrating by parts, we obtain.
$\text{I}=\int\text{x}\sin\text{x dx}-\int\Bigg\{\Big(\frac{\text{d}}{\text{dx}}\text{x}\Big)\int\sin\text{x dx}\Bigg\}\text{dx}$
$=\text{x}(-\cos\text{x})-\int1.(-\cos\text{x})\text{dx}$
$=-\text{x}\cos\text{x}+\sin\text{x}+\text{C}$
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