Lösungen/Solutions/I1S2AnUe/Ex6

L = Lektion/ Leçon   -- Sprechstunde / heures de consultation
W = Work / Arbeit / Travail
A=Anhang/Annexe/Appendice

Probl/Ex 1      W

r[φ_] := (E^φ Sin[φ] (2 + φ))

Integrate[r[φ]^2 /2, {φ, 0, Pi}]

N[%]

Probl/Ex 2      W

Integrate[
      Evaluate[Sqrt[
          r[φ]^2 + 
            D[r[φ], φ]^2]], {φ, 0, 
        Pi}]

NIntegrate[
      Evaluate[Sqrt[
          r[φ]^2 + 
            D[r[φ], φ]^2]], {φ, 0, 
        Pi}]

Probl/Ex 3      W

f[x_] := (E^x Sin[x] (2 + x))

Integrate[Evaluate[Sqrt[1 + D[f[x], x]^2]], {x, 0, Pi}]

NIntegrate[Evaluate[Sqrt[1 + D[f[x], x]^2]], {x, 0, Pi}]

Probl/Ex 4      W

v[t_] := {4 Sin[t], 7 Cos[t],  t^2}

D[v[t], t]

vLen[v_] := Sqrt[v . v]

vLen[D[v[t], t]]

Integrate[Evaluate[vLen[D[v[t], t]]], {t, 0, 4}]

NIntegrate[Evaluate[vLen[D[v[t], t]]], {t, 0, 4}]

Probl/Ex 5      W

?Apart

Apart[1/((x - a) (x - b) (x - c))]

Integrate[1/((x - a) (x - b) (x - c)), x]