Question
Download Solution PDF\(\int^{-1}_{-2}\frac{x}{|x|}dx\) किसके बराबर है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
f(x) = |x| निम्न के बराबर होगा
- x, यदि x > 0
- -x, यदि x < 0
- 0, यदि x = 0
∫ dx = x + C (C स्थिरांक है।)
∫ xn dx = xn+1/n+1 + C
गणना:
माना कि \(I = \int^{-1}_{-2}\frac{x}{|x|}dx\) है।
उपरोक्त संकल्पना का प्रयोग करने पर, x ∈ (-2, -1) के रूप में
⇒ \(I=∫^{-1}_{-2}\frac{x}{-x}dx\)
⇒ \(I=-1∫^{-1}_{-2}(1)dx\)
⇒ \(I=-[x]^{-1}_{-2}\)
⇒ I = -[-1 - (-2)]
∴ \(\int^{-1}_{-2}\frac{x}{|x|}dx\) = -1
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