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Question Number 86138 by jagoll last updated on 27/Mar/20

$$\int \underset{-4}{\stackrel{8}{}}\frac{\mid \mathrm{x}\mid }{\mathrm{x}}\mathrm{dx}=?$$

Commented by Prithwish Sen 1 last updated on 27/Mar/20

$$\mathrm{l}\underset{ϵ\to 0}{\mathrm{t}}\{{\int }_{-4}^{ϵ}(-1)\mathrm{dx}+{\int }_{ϵ}^8\mathrm{dx}\}$$$$={\mathrm{lt}}_{ϵ\to 0}\{-ϵ-4+8-ϵ\}={\mathrm{lt}}_{ϵ\to 0}\{4-2ϵ\}=4$$$$\mathbf{please}\mathbf{check}.$$

Answered by TANMAY PANACEA. last updated on 27/Mar/20

$${\int }_{-4}^0\frac{-x}{x}dx+{\int }_0^8\frac{x}{x}dx$$$$-1\times (0+4)+(8-0)=4$$

Commented by jagoll last updated on 27/Mar/20

$$\mathrm{yes}\mathrm{sir}.\mathrm{i}\mathrm{got}\mathrm{same}\mathrm{result}$$

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