Rajasthan Boardहिन्दी माध्यमकक्षा 12 साइन्सगणितसमाकलन2 Marks
Question
समाकलन को ज्ञात कीजिए $x \sqrt{1+2 x^{2}}$
✓
Answer
माना l $= \int x \sqrt{1+2 x^{2}} d x$
माना $1 + 2x^{2 }= t$
$x$ के सापेक्ष अवकलन करने पर,
$4x = \frac{d t}{d x} \Rightarrow d x=\frac{d t}{4 x}$
$\therefore I=\int x \sqrt{t} \frac{d t}{4 x} =\frac{1}{4} \int \sqrt{t} d t =\frac{1}{4} \int t^{\frac1 2} d t =\frac{1}{4} \frac{t^{(\frac1 2)+1}}{(\frac1 2)+1}+C =\frac{1}{6}\left(1+2 x^{2}\right)^{\frac3 2}+ C$
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