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How Much to Spend on Rent - AssociationVoting

📅 May 17, 2026 👤 scraface

May 17, 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 \( \int_0^2 [(4x - x^2) - x^2] \, dx = \int_0^2 (4x - 2x^2) \, dx \).

📌 Integrate:

📌 \( \left[2x^2 - rac{2}{3}x^3

📌 ight]_0^2 = \left(2(4) - rac{2}{3}(8)

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