CBSE Boardहिन्दी माध्यमकक्षा 12 साइन्सगणितसमाकलन2 Marks
Question
समाकलन को ज्ञात कीजिए: $\int\left(\sqrt{x}-\frac{1}{\sqrt{x}}\right)^{2} d x$
✓
Answer
$\int\left(\sqrt{x}-\frac{1}{\sqrt{x}}\right)^{2} d x$$=\int\left[(\sqrt{x})^{2}+\left(\frac{1}{\sqrt{-x}}\right)^{2}-2 \sqrt{x} \times \frac{1}{\sqrt{x}}\right] d x$ [$\because (a - b)^2 = a^2 + b^2 - 2ab]$
$=\int\left(x+\frac{1}{x}-2\right) d x$ $=\int x d x+\int \frac{1}{x} d x$$-2 \int 1 d x=\frac{x^{2}}{2} + log |x| − 2x + C$
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