# Are these correct?

#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))
``````

# [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. 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. ]