Rajasthan Boardहिन्दी माध्यमकक्षा 12 साइन्सगणितसमाकलन2 Marks
Question
फलन का समाकलन ज्ञात कीजिए: cot x log sin x
✓
Answer
$\int$cot x log sin x dx माना log sin x = t $ \Rightarrow \frac{1}{\sin x} \times \cos x$ $=\frac{d t}{d x} \Rightarrow \cot x$ $=\frac{d t}{d x} \Rightarrow d x$ $=\frac{d t}{\cot x}$ $\therefore$ $\int \cot x \log \sin x d x$ $=\int \cot x \cdot t $ $\frac{d t}{\cot x}=\int t d t$ $=\frac{t^{2}}{2}+C$ $=\frac{(\log \sin x)^{2}}{2}$ + C
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