Question Number 134764 by bramlexs22 last updated on 07/Mar/21
$$\:\mathbb{Z}\:=\:\int_{\mathrm{0}} ^{\:\mathrm{2}} \:\frac{\mathrm{dx}}{\:\sqrt{\mid\mathrm{x}−\mathrm{1}\mid}}\:? \\ $$
Answered by EDWIN88 last updated on 07/Mar/21
![Z = ∫_0 ^( 2) (dx/( (√(∣x−1∣)))) ; let u=∣x−1∣ Z= ∫_(−1) ^( 1) (du/( (√u))) = 2∫_0 ^( 1) (du/( (√u))) = 4 [ (√u) ]_0 ^1 Z = 4](Q134765.png)
$$\mathbb{Z}\:=\:\int_{\mathrm{0}} ^{\:\mathrm{2}} \:\frac{\mathrm{dx}}{\:\sqrt{\mid\mathrm{x}−\mathrm{1}\mid}}\:;\:\mathrm{let}\:\mathrm{u}=\mid\mathrm{x}−\mathrm{1}\mid \\ $$$$\mathbb{Z}=\:\int_{−\mathrm{1}} ^{\:\mathrm{1}} \frac{\mathrm{du}}{\:\sqrt{\mathrm{u}}}\:=\:\mathrm{2}\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{du}}{\:\sqrt{\mathrm{u}}}\:=\:\mathrm{4}\:\left[\:\sqrt{\mathrm{u}}\:\right]_{\mathrm{0}} ^{\mathrm{1}} \\ $$$$\mathbb{Z}\:=\:\mathrm{4} \\ $$