Gujarat BoardEnglish MediumSTD 12 ScienceMathsINTEGRALS2 Marks
Question
$\int\sin^2\frac{\text{x}}{2}\text{dx}$
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Answer
Let I $=\int\sin^2\frac{\text{x}}{2}\text{dx}.$ Then, $\text{I}=\frac{1}{2}\int2\sin^2\frac{\text{x}}{2}\text{dx}$ $=\frac{1}{2}\int(1-\cos\text{x})\text{dx}$$[\because\cos2\text{x}=1-2\sin^2\text{x}]$ $=\frac{1}{2}\int\text{dx}-\frac{1}{2}\int\cos\text{xdx}$ $=\frac{1}{2}\times\text{x}-\frac{1}{2}\times\sin\text{x}+\text{C}$ $=\frac{1}{2}(\text{x}-\sin\text{x})+\text{C}$ $\therefore\text{I}=\frac{1}{2}(\text{x}-\sin\text{x})+\text{C}$
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