Gujarat BoardEnglish MediumSTD 12 ScienceMathsINTEGRALS3 Marks
Question
Integrate the function in exercise. $\text{x}^2 \ \text{e}^\text{x}$
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Answer
Let $\text{I}=\int\text{x}\sin3\text{x dx}$ Taking x2 as first function and ex as second function and integrating by parts, we obtain. $\text{I}=\text{x}\int\sin3\text{x dx}-\int\Bigg\{\Big(\frac{\text{d}}{\text{dx}}\text{x}\Big)\int\sin3\text{x dx}\Bigg\}$ $=\text{x}\Big(\frac{-\cos3\text{x}}{3}\Big)-\int1.\Big(\frac{-\cos3\text{x}}{3}\Big)\text{dx}$ $=\frac{-\text{x}\cos3\text{x}}{3}+\frac{1}{3}\int\cos3\text{x} \ \text{dx}$ $=\frac{-\text{x}\cos3\text{x}}{3}+\frac{1}{9}\sin3\text{x} \ \text{dx}+\text{C}$
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