Rajasthan Boardहिन्दी माध्यमकक्षा 12 साइन्सगणितसमाकलन2 Marks
Question
$\int_{-4}^4|x| d x$ का मान लिखिए।
✓
Answer
माना $ I =\int_{-4}^4|x| d x=\int_{-4}^0|x| d x+\int_0^4|x| d x$
$\because|x|=\left\{\begin{array}{l}x, x>0 \\ -x, x<0\end{array}\right.$
$\therefore I =\int_{-4}^0-x d x+\int_0^4 x d x$
$=\left[\frac{-x^2}{2}\right]_{-4}^0+\left[\frac{x^2}{2}\right]_0^4$
$=\frac{-1}{2}[0-16]+\frac{1}{2}[16-0]$
$=8+8$
$=16$
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