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x-dx-




Question Number 8914 by tawakalitu last updated on 04/Nov/16
∫ ∣x∣ dx
$$\int\:\mid\mathrm{x}\mid\:\mathrm{dx} \\ $$
Commented by 123456 last updated on 05/Nov/16
I=∫∣x∣dx  x>0  I=∫xdx=(x^2 /2)+C  x<0  I=−∫xdx=−(x^2 /2)+C  ∫∣x∣dx=((sign(x)x^2 )/2)+C
$${I}=\int\mid{x}\mid{dx} \\ $$$${x}>\mathrm{0} \\ $$$${I}=\int{xdx}=\frac{{x}^{\mathrm{2}} }{\mathrm{2}}+{C} \\ $$$${x}<\mathrm{0} \\ $$$${I}=−\int{xdx}=−\frac{{x}^{\mathrm{2}} }{\mathrm{2}}+{C} \\ $$$$\int\mid{x}\mid{dx}=\frac{\mathrm{sign}\left({x}\right){x}^{\mathrm{2}} }{\mathrm{2}}+{C} \\ $$
Commented by tawakalitu last updated on 05/Nov/16
Thanks sir. God bless you.
$$\mathrm{Thanks}\:\mathrm{sir}.\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}. \\ $$

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