| Integral of a Variable and it's Formulas - I and II - Code |

Dec. 21, 2024, 2:03 p.m.

 

 

 

 

1. What is the python code for this problem:

# 1st: Import the sympy module
import sympy as sp  # Import sympy for symbolic mathematics

# 2nd: Define the variable 'z'
z = sp.symbols('z')  # Define 'z' as a symbolic variable

# 3rd: Define the integrand
integrand = ((9 - sp.sqrt(z))**4) / sp.sqrt(z)  # Define the integrand function

# 4th: Perform the integration
integral = sp.integrate(integrand, z)  # Compute the indefinite integral

# 5th: Display the result
sp.pprint(integral)  # Pretty print the result

 

 

 

 

2. What is the python code for this problem:

# 1st: Import the sympy module
import sympy as sp  # Import sympy for symbolic mathematics

# 2nd: Define the variable 'm'
m = sp.symbols('m')  # Define 'm' as a symbolic variable

# 3rd: Define the integrand
integrand = 1 / (m**3 * sp.sqrt(sp.ln(m)))  # Define the integrand function

# 4th: Perform the integration
integral = sp.integrate(integrand, m)  # Compute the indefinite integral

# 5th: Display the result
sp.pprint(integral)  # Pretty print the result

 

 

 

 

3. What is the python code for this problem:

# 1st: Import the sympy module
import sympy as sp  # Import sympy for symbolic mathematics

# 2nd: Define the variable 'x'
x = sp.symbols('x')  # Define 'x' as a symbolic variable

# 3rd: Define the integrand
integrand = (sp.exp(x) + sp.exp(-x)) / sp.sqrt(3 * sp.exp(x) - sp.exp(-x))  
# Define the integrand function

# 4th: Perform the integration
integral = sp.integrate(integrand, x)  # Compute the indefinite integral

# 5th: Display the result
sp.pprint(integral)  # Pretty print the result

 

 

 

 

4. What is the python code for this problem:

# 1st: Import the sympy module
import sympy as sp  # Import sympy for symbolic mathematics

# 2nd: Define the variable 'c'
c = sp.symbols('c')  # Define 'c' as a symbolic variable

# 3rd: Define the integrand
f = (1 - c**3)**2 * c  # Define the function to integrate

# 4th: Perform the integration
integral = sp.integrate(f, c)  # Compute the indefinite integral

# 5th: Display the result
sp.pprint(integral)  # Pretty print the result

 

 

 

 

5. What is the python code for this problem:

# 1st: Import the sympy module
import sympy as sp  # Import sympy for symbolic mathematics

# 2nd: Define the variable 'n'
n = sp.symbols('n')  # Define 'n' as a symbolic variable

# 3rd: Define the integrand
f = n**3 * sp.sqrt(n**4 - 5)  # Define the function to integrate

# 4th: Perform the integration
integral = sp.integrate(f, n)  # Compute the indefinite integral

# 5th: Display the result
sp.pprint(integral)  # Pretty print the result
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