intexo.py

Created on March 20, 2022
1.56 KB
Exo 1:
      1                                             1
  I= S  (2x+2)dx =  [2*1/2*x**2   +2x] =  [x**2 +2x]
     -1                                            -1
= (1+2)-(1-2)=4

      1
  J= S  (x+1)e**x dx      ->  J=e+e**-1
     -1
                      1    1
  J= // = [(x+1)*e**x]  - S  (1*e**x)DX
                     -1   -1
                                    1
((1+1)e**1) - ((-1+1)e**-1) - [e**x]  = 2e-(e**1 - e**-1) = e+e**-1
                                   -1      

K=J+I = e+e**-1 + 4
-> k est la valeur en unite d air comprise 
entre la courbe c, l axe des abscisses et les droites 
d equations x=-1 et x=1. 

Exo 3:
   3          -> 1/at+b = 1/a* ln(at+b)    3
A=S 5/2x+3 dx  = 5* 1/2x+3 = [5/2 ln(2x+3)]  = 5/2 *ln(2*3+3) - (5/2 ln(2*1+3))
   1                                       1
  = 5/2 (ln(9/5))
  
   0          -> u'cosu  
B=S     -2cos(2x+pi/4)dx = -2 * (1/2* sin(2x+pi/4)) = [sin(2x+pi/4)]
  -pi/2  
 =-((sin2*0+pi/4) - (sin2*-pi/2+pi/4)) = -sqrt2
 
   1/3               -> u'e**u = e**u                          
C=S   3e**-3x+1 dx = -[e**-3x+1] = -(e**-3*1/3+1   -e**-3*0+1) =e-1
   0
                    
   2                ->u'/u**2 = -1/u           2
D=S x-1/(x**2-2x+3)**2 dx = 1/2 S 2x-2/(x**2-2x+3)**2 = 1/2[-1/(x**2 -2x+3)] 
   1                             1

   pi/3                                    pi/3
E=S     xsin(3x)dx = [x*(-1/3)*cos(3x)] - S     1*(-1/3)*cos(3x)dx
   0                                       0
 = (pi/3*(-1/3)cos(3*pi/3)) - (0*(-1/3)cos(3*0)) - [sin3x]
 = -pi/9cos(pi) - (sin(3*pi/3))-(sin(3*0))
 = pi/9