531.sagews

h, v, m = var('h v m')
assume(h > 0)
assume(m > h/2)
1/h^2*(integral((h - 2*v)/4, v, 0, h/2)+ integral((2*v - h)/4, v, h/2, (4*m - h)/2) + integral((v - m), v, (4*m - h)/2, h))

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{\frac{\frac{{16 {m}^{2} } - {{16 h} m} + {3 {h}^{2} }}{4} + \frac{{h}^{2} }{4}}{4} + \frac{{{4 h} m} - {h}^{2} }{8} + \frac{{h}^{2} - {{2 h} m}}{2} + \frac{{h}^{2} }{16}}{{h}^{2} }

h, v, m = var('h v m')
assume(h > 0)
assume(m > h/2)
1/h^2*(integral((h - 2*v)/4, v, 0, h/2)+ integral((2*v - h)/4, v, h/2, (4*m - h)/2) + integral((h - v), v, (4*m - h)/2, h))

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{\frac{\frac{{16 {m}^{2} } - {{16 h} m} + {3 {h}^{2} }}{4} + \frac{{h}^{2} }{4}}{4} + \frac{{16 {m}^{2} } - {{24 h} m} + {5 {h}^{2} }}{8} + \frac{{9 {h}^{2} }}{16}}{{h}^{2} }

h, v, m = var('h v m')
assume(h > 0)
assume(m < h/2)
1/h^2*(integral((h - 2*v)/4, v, 0, (4*m - h)/2)+ integral(m - v, v, (4*m - h)/2, m) + integral((h - v), v, m, h))

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{\frac{{m}^{2} - {{2 h} m}}{2} + \frac{{m}^{2} }{2} + \frac{{-16 {m}^{2} } + {{16 h} m} - {3 {h}^{2} }}{16} + \frac{{h}^{2} - {{4 h} m}}{8} + \frac{{h}^{2} }{2}}{{h}^{2} }

h, v, m = var('h v m')
assume(h > 0)
assume(m > h/2)
1/h^2*(integral((h - 2*v)/4, v, 0, (4*m - h)/2)+ integral(m - v, v, (4*m - h)/2, m) + integral((v - m), v, m, h))

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{{m}^{2} + \frac{{-16 {m}^{2} } + {{16 h} m} - {3 {h}^{2} }}{16} + \frac{{h}^{2} - {{2 h} m}}{2} + \frac{{h}^{2} - {{4 h} m}}{8}}{{h}^{2} }

h, x, y, m = var('h x y m')
assume(h > 0)
assume(x > m)
1/h*(integral((4*x - h)/4 - y/2, y, 0, (4*m - h)/2)+ integral((x - m), y, (4*m - h)/2, h))

\newcommand{\Bold}[1]{\mathbf{#1}}-\frac{1}{16} \, \frac{{(8 \, {(m - x)} {(3 \, h - 4 \, m)} + 8 \, {(h - 4 \, m)} x - h^{2} + 16 \, m^{2})}}{h}