Question
Download Solution PDFWhat is \(\int^{-1}_{-2}\frac{x}{|x|}dx\) equal to?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
f(x) = |x| will be equal to
- x, if x > 0
- -x, if x < 0
- 0, if x = 0
∫ dx = x + C (C is a constant)
∫ xn dx = xn+1/n+1 + C
Calculation:
Let, \(I = \int^{-1}_{-2}\frac{x}{|x|}dx\)
Using the above concept, as x ∈ (-2, -1)
⇒ \(I=∫^{-1}_{-2}\frac{x}{-x}dx\)
⇒ \(I=-1∫^{-1}_{-2}(1)dx\)
⇒ \(I=-[x]^{-1}_{-2}\)
⇒ I = -[-1 - (-2)]
∴ \(\int^{-1}_{-2}\frac{x}{|x|}dx\) = -1
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