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Find the area of the region bounded by the graphs of the equations [tex]y=2x-x^2, y=0.[/tex] Provide a sketch. Show the work!

Answer :

[tex]\\ \sf\longmapsto y=2x-x^2[/tex]

  • y=0

[tex]\\ \sf\longmapsto 2x-x^2=0[/tex]

[tex]\\ \sf\longmapsto x^2-2x=0[/tex]

[tex]\\ \sf\longmapsto x(x-2)=0[/tex]

[tex]\\ \sf\longmapsto x=0,2[/tex]

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Answer

⇒ y=2x−x2

  • y=0

⇒ 2x - x² = 0

⇒ x² - 2x = 0

⇒ x ( x - 2 ) = 0

⇒ x = 0, 2

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