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Обчисли площу фігури, обмеженої лініями y=4x^(2),y=14sqrtx". "

Обчисли площу фігури, обмеженої лініями\newliney=4x2,y=14x.  y=4 x^{2}, y=14 \sqrt{x} \text {. }

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Q. Обчисли площу фігури, обмеженої лініями\newliney=4x2,y=14x.  y=4 x^{2}, y=14 \sqrt{x} \text {. }
  1. Set up integral: Set up the integral for the area between the curves.\newlineFind the points of intersection by setting 4x2=14x4x^2 = 14\sqrt{x}.\newline4x2=14x4x^2 = 14\sqrt{x}
  2. Find points of intersection: Solve for xx in the equation 4x2=14x4x^2 = 14\sqrt{x}.\newlineSquare both sides to remove the square root:\newline(4x2)2=(14x)2(4x^2)^2 = (14\sqrt{x})^2\newline16x4=196x16x^4 = 196x

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