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compromise of 1877 - NBX Soluciones

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 To find the area of the region enclosed by the curves \( y = x^2 \) and \( y = 4x - x^2 \), we first determine the points of intersection by setting the equations equal:

📌 x^2 = 4x - x^2.

📌 2x^2 - 4x = 0.

📌 Factoring out \( 2x \):

📌 2x(x - 2) = 0.

📌 Thus, the points of intersection are \( x = 0 \) and \( x = 2 \).

📌 The area \( A \) between the curves from \( x = 0 \) to \( x = 2 \) is given by:

📌 A = \int_0^2 \left((4x - x^2) - x^2\right) \, dx = \int_0^2 (4x - 2x^2) \, dx.

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