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Question Number 206391 by hardmath last updated on 13/Apr/24

$$\mathrm{Find}:$$$${\int }_{-3}^{-2}(\mid \mathrm{x}\mid +\mid \mathrm{x}-4\mid )\mathrm{dx}=?$$

Answered by MM42 last updated on 13/Apr/24

$$I={\int }_{-3}^{-2}(-2x+4)dx$$$${=(-x^2+4x)]}_{-3}^{-2}=-12+21=9✓$$$$$$

Answered by TonyCWX08 last updated on 13/Apr/24

$$\underset{-3}{\stackrel{-2}{\int }}(\mid x\mid +\mid x-4\mid )dx$$$$=\underset{-3}{\stackrel{-2}{\int }}(\mid x\mid )dx+\underset{-3}{\stackrel{-2}{\int }}(\mid x-4\mid )dx$$$$=\underset{-3}{\stackrel{-2}{\int }}(-x)dx+\underset{-3}{\stackrel{-2}{\int }}-(x-4)dx$$$$\text{Missing left or extra right}$$$$=(-2+\frac{9}{2})+(-10+\frac{33}{2})$$$$=\frac{5}{2}+\frac{13}{2}$$$$=9$$

Commented by hardmath last updated on 13/Apr/24

$$\mathrm{thank}\mathrm{you}\mathrm{dear}\mathrm{professors}\mathrm{cool}$$

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