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Home » You Won’t Believe What Longinus Achieved Centuries Before His Time! - Abbey Badges

You Won’t Believe What Longinus Achieved Centuries Before His Time! - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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Find the area enclosed by the curves \( y = x^2 \) and \( y = 4x - x^2...
Set the equations equal to find intersection points:
\( x^2 = 4x - x^2 \Rightarrow 2x^2 - 4x = 0 \Rightarrow 2x(x - 2) = 0...
So, \( x = 0 \) and \( x = 2 \).
The area is \( \int_0^2 [(4x - x^2) - x^2] \, dx = \int_0^2 (4x - 2x^2...
Integrate:
\( \left[2x^2 - rac{2}{3}x^3
ight]_0^2 = \left(2(4) - rac{2}{3}(8)
ight) - 0 = 8 - rac{16}{3} = rac{24}{3} - rac{16}{3} = rac{8}{3} \...
So, the enclosed area is \( rac{8}{3} \) square units.

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