MCQ
$\int\limits_a^b {{\mathop{\rm sgn}} \,x} \,\,dx$ $=$ (where $a, b \in R$)
- A$| b | - | a |$
- B$(b-a)\, sgn\, (b-a)$
- C$b\, sgnb - a\, sgna$
- ✓Both $(A)$ and $(C)$
$a<0$ $b>0$
$I=\int_{a}^{b} \int \operatorname{sgn}(x) d x= \int_{a}^{0}(-1) d x+\int_{0}^{b}(1) d x$
$\geqslant-[x]_{a}^{0}+[x]_{0}^{b}$
$>-(0-a)+(b-0)$
$x a^{0}+b$
If $a \cdot \operatorname{sgn}(a)+b \operatorname{sgn}(b)$
$a>0, \quad b>0$
$I=\int_{a}^{b} 1 d x=[x]_{a}^{b}=b-a$
$\int_{a}^{b} \operatorname{sgn}(x) d x=|b|-|a|$
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