求曲線 y^2=x(x−4)^2 所圍成的面積。

所求＝\(\displaystyle2\int_0^4x^{1/2}\left(4-x\right)dx=2\int_0^4\left(4x^{1/2}-x^{3/2}\right)dx=2\left(\frac{8}{3}x^{3/2}-\frac{2}{5}x^{5/2}\right)\Bigg|_0^4=\frac{256}{15}\)