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#c) Compute the integral ∫05 x^3 + 2*x^2 dx sympy

       #import the modul

       from sympy import *

        #symbole for x

          x = symbols('x')

          # x^3 + 2x^2

          expr = (x**3) + 2*(x**2)

          #integrate exp from 0 to 5

          value = integrate(expr,(x,0,5))

          #out the value

        print ('The value of the definate integral = ', float (value))

#d) Compute the matrix product [ [1.0,0.0], [2.0, 5.0] *[1.5,2.0], [2.0, 2.0]]

   import numpy as np

 

  a = np.array([[1.0, 0.0], [2.0, 5.0]])

   b = np.array( [[1.5,2.0], [2.0, 2.0]])

 

    print (np.dot(a,b))

d result : [[ 1.5 2. ]

[13. 14. ]]

#e) Create a 7 by 7 identity matrix using numpy.

      import numpy as np

      I = np.identity(7)

     print(I)

#result:[[1. 0. 0. 0. 0. 0. 0.]

[0. 1. 0. 0. 0. 0. 0.]

[0. 0. 1. 0. 0. 0. 0.]

[0. 0. 0. 1. 0. 0. 0.]

[0. 0. 0. 0. 1. 0. 0.]

[0. 0. 0. 0. 0. 1. 0.]

[0. 0. 0. 0. 0. 0. 1.]]

#f)Compute the inverse of the matrix [[1.5, 2.0], [2.0, 2.0]]

#Import required package

   import numpy as np

    #Taking a 2 * 2 matrix

    A = np.array([[1.5, 2.0],

          [2.0, 2.0]])

       #Calculating the inverse of the matrix

         print(np.linalg.inv(A))

#result : [[-2. 2. ]

[ 2. -1.5]]