CBSE Boardहिन्दी माध्यमकक्षा 12 साइन्सगणितसमाकलन2 Marks
Question
$\int_0^\pi \sin ^2 x d x$ का मान लिखिए।
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Answer
माना $\quad I =\int_0^\pi \sin ^2 x d x=\int_0^\pi\left(\frac{1-\cos 2 x}{2}\right) d x$ $\quad$$I =\frac{1}{2}\left[x-\frac{\sin 2 x}{2}\right]_0^\pi$ $\quad$$\quad$$=\frac{1}{2}\left[\left(\pi-\frac{1}{2} \sin 2 \pi\right)-(0-0)\right]$ $\quad$$\quad$$=\frac{1}{2}[\pi-0]=\frac{\pi}{2}$
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