TP Maple : Int´egration
MPSI-Maths.
Mr Mamouni: [email protected]
Source disponible sur :
http://www.chez.com/myismailc
Calcul de primitive.
> int( sin(x), x );
−cos(x)
Int´egration par partie. Il faut pr´eciser en Maple la fonction v, lui se charge de u’
> with(student):
> intparts(Int(x^k*ln(x), x), ln(x));
ln(x)x(k+1) k+ 1 −
Z x(k+1) x(k+ 1)dx Changement de variable. Il faut le pr´eciser Maple
> changevar(cos(x)+1=u, Int((cos(x)+1)^3*sin(x), x), u);
Z
−u3du
Somme de Riemann `a gauche
> leftbox(sin(x)*x+sin(x), x=0..2*Pi, 5, shading=BLUE);
> leftsum(sin(x)*x+sin(x), x=0..2*Pi, 5);
2 5π
4
X
i=0
(2 5sin(2
5i π)i π+ sin(2 5i π))
!
Somme de Riemann `a droite
> rightbox(sin(x)*x+sin(x), x=0..2*Pi, 5, shading=BLUE);
> rightsum(sin(x)*x+sin(x), x=0..2*Pi, 5);
2 5π
5
X
i=1
(2 5sin(2
5i π)i π+ sin(2 5i π))
!
Somme de Riemann au milieu
> middlebox(sin(x)*x+sin(x), x=0..2*Pi, 5, shading=BLUE);
> middlesum(sin(x)*x+sin(x), x=0..2*Pi, 5);
2 5π
4
X
i=0
(2 5sin(2
5(i+ 1
2)π) (i+ 1
2)π+ sin(2 5(i+ 1
2)π))
!
M´ethode des trap`ezes.
> trapezoid(x^k*ln(x), x=1..3);
1 2
3
X
i=1
(1 + 1
2i)kln(1 + 1 2i)
! +1
43kln(3) M´ethode de Simpson.
> simpson(x^k*ln(x), x=1..3);
1
63kln(3) +2 3
2
X
i=1
(i+1
2)kln(i+1 2)
! +1
3(
1
X
i=1
(1 +i)kln(1 +i))
Fin.
MPSI-Maths Mr Mamouni
TP Maple: Int´egration.
Page 1 sur 1
http://www.chez.com/myismail [email protected]
