(%i1) "Mathe Q1: Cornelsen, S. 210, Nr. 7"$

(%i2) "a) Stammfunktion von f(x) = (x^2 - 2*x) * exp(0.5*x)"$

(%i3) (x^2 - 2*x) * exp(0.5*x);
                                2          0.5 x
(%o3)                         (x  - 2 x) %e

(%i4) integrate((x^2 - 2*x) * exp(0.5*x),x);

                      2               x/2                 x/2
(%o4)             (2 x  - 8 x + 16) %e    - 2 (2 x - 4) %e

(%i5) "b) gelbe Flaeche A"$

(%i6) (x^2 - 2*x) = 0;
                                  2
(%o6)                            x  - 2 x = 0

(%i7) solve((x^2 - 2*x) = 0,x);
(%o7)                           [x = 0, x = 2]

(%i8) ev(%,numer);
(%o8)                           [x = 0, x = 2]

(%i9) integrate( (x^2 - 2*x) * exp(0.5*x),x,0,2);

(%o9)                              8 %e - 24

(%i10) ev(%,numer);
(%o10)                        - 2.253745372327639

(%i11) "c) Verhaeltnis der Flaechen A_1 und A_2, geteilt durch x=1"$

(%i12) integrate( (x^2 - 2*x) * exp(0.5*x),x,0,1);

(%o12)                         14 sqrt(%e) - 24

(%i13) ev(%,numer);
(%o13)                        - 0.91790221019821

(%i14) 0.91790221019821/(2.253745372327639-0.91790221019821);
(%o14)                         0.68713321759645

(%i15) (2.253745372327639-0.91790221019821)/0.91790221019821;
(%o15)                         1.455321871205615