>>204

sin(a)=t-a0 < x < a
V1=π{(sin(x))^2}dx=(π/2){a-(1/2)sin(2a)}

a < x < tV2=π{(tx)^2}dx=π{(1/3)x^3-tx^2+t^2x}
=π{(1/3)t^3-(1/3)a^3+ta^2-t^2a}

V=π{(1/2)a-(1/4)sin(2a)+(1/3)t^3-(1/3)a^3+ta^2-t^2a}
=π{(1/2)a-(1/4)sin(2a)+(1/3)(sin(a))^3}

dV/da=π{(1/2)-(1/2)cos(2a)+(sin(a))^2cos(a)}
dV/dt=π{(1/2)-(1/2)cos(2a)+(sin(a))^2cos(a)}/(1+cos(a))=π/4
4(cos(a))^3+4(cos(a))^2-3cos(a)-3=(4(cos(t))^2-3)(cos(t)+1)=0

a=π/6
V=π{π/12-√(3)/8+(1/24)}

a=5π/6
V=π{5π/12+√(3)/8+(1/24)}