Lösungen/Solutions/
B2S2Ue/Ex13

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

Probl/Ex 1      W

ln[x_] := Log[x]

a

Integrate[(3  x + 5)^1000, x]

Integrate[(3  x + 5)^1000, {x, 1, 2}]

Integrate[(3  x + 5)^1000, {x, 1, 2}] // N

b

Integrate[ln[x]^2 / x, x]

Integrate[ln[x]^2 / x, {x, 1, 2}]

% // N

c

Integrate[x (E^(x^2))^2, x]

Integrate[x (E^(x^2))^2, {x, 0, 1}]

% // N

Probl/Ex 2      W

A = Integrate[2 Pi E^x Sqrt[1 + E^x], x]

A = 
      Integrate[2 Pi E^x Sqrt[1 + E^x], {x, -Infinity, 0}]

A = 
      Integrate[
          2 Pi E^x Sqrt[1 + E^x], {x, -a, 
            0}] //. {(E^(-a)) (1 + (E^a)) -> 
            E^(-a) + 1, 
          Sqrt[(E^(-a)) (1 + (E^a))] -> 
            Sqrt[E^(-a) + 1]}

A = 
      Limit[Integrate[
            2 Pi E^x Sqrt[1 + E^x], {x, -a, 
              0}] //. {(E^(-a)) (1 + (E^a)) -> 
              E^(-a) + 1, 
            Sqrt[(E^(-a)) (1 + (E^a))] -> Sqrt[E^(-a) + 1]}, a -> Infinity]

V = Integrate[(E^x)^2 Pi, x]

Integrate[(E^x)^2 Pi, {x, -Infinity, 0}]

Probl/Ex 3      W

f3[x_] := 1 - x^2

Solve[f3[x] == 0, {x}]

V = Integrate[f3[x]^2 Pi, {x, -1, 1}]

N[%]

Probl/Ex 4      W

solv4 = Solve[z == 4 - x^2 - y^2, {y}] // Flatten

OutputForm[%]

f4[x_, z_] := Evaluate[y /. solv4[[2]]]

f4[u, v]

Integrate[Evaluate[f4[0, v]^2 Pi], v]

Integrate[Evaluate[f4[0, v]^2 Pi], {v, 0, 4}]