Integral CAS approximation

[Albert Chan]

On HP emulator, integration seems work harder if we use pattern ∫(f(x), x= a .. b)

We integrate ∫(√(1+x^3), x= -1 .. 1) backwards (*), letting t = -x

Cas> expand(∫(√(1-t^3), t, -1, 1))

√2*2*1/5 + integrate(3/5/√(-t^3+1),t,-1,1)

Cas> float(Ans)       → 1.95275719206

Cas> expand(∫(√(1-t^3), t = -1 .. 1))

√2*2*1/5 + 1/5*√π*Gamma(1/3)/Gamma(5/6) + integrate(3/5/√(-t^3+1),t,-1,0)

Cas> float(Ans)       → 1.95275723373


(*) Cas knows ∫(√(1-t^3), t,0,1), but not its equivalent, ∫(√(1+x^3), x,-1,0)