Signum Integral

Calculus Level 4

∫ a b sgn(x) dx = ? \large \displaystyle\int_a^b \text{sgn(x) dx} = \ ?

Details :
- sgn ( x ) \text{sgn}(x) denotes the signum function of x x
- sgn ( x ) = { 1 , x > 0 0 , x = 0 − 1 , x < 0 \text{sgn}(x) = \begin{cases} 1 \quad,\quad x>0 \\ 0 \quad,\quad x=0 \\ -1 \quad,\quad x<0 \end{cases}
- a , b ∈ ℜ a , b \in \Re

( b − a ) sgn ( b − a ) (b - a)\text{sgn}(b - a) b ⋅ s g n ( b ) + a ⋅ s g n ( a ) b\cdot sgn(b) + a\cdot sgn(a) ( b + a ) sgn ( b − a ) (b + a)\text{sgn}(b - a ) b ⋅ s g n ( b ) − a ⋅ s g n ( a ) b\cdot sgn(b) - a\cdot sgn(a)

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Akhil Bansal by Akhil Bansal , 22, India

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1 solution

Abhinav Jha
Dec 29, 2015

In IIT style Start checking options one by one. When a & b both >0 or <0 area in closed will be (b - a) For cases also area is same. Option b sgn(b) - a sgn(a). Is correct

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