| Trigonometric Substitution - Code |

Dec. 21, 2024, 3:53 p.m.

 

 

 

 

1. What is the python code for this problem:

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

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

# 3rd: Define the integrand
integrand = (m**3 - 2) / m  # Define the function to integrate

# 4th: Perform the integration with respect to 'm'
integral_result = sp.integrate(integrand, m)  # Compute the integral

# 5th: Display the result
print(integral_result)  # Print the result of the integral

 

 

 

 

2. What is the python code for this problem:

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

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

# 3rd: Define the integrand
integrand = (sp.ln(x) + 4) / x**2  # Define the function to integrate

# 4th: Perform the integration with respect to 'x'
integral_result = sp.integrate(integrand, x)  # Compute the integral

# 5th: Display the result
print(integral_result)  # Print the result of the integral

 

 

 

 

3. What is the python code for this problem:

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

# 2nd: Define the variable 's'
s = sp.symbols('s')  # Define the symbolic variable 's'

# 3rd: Define the integrand
integrand = s / sp.sqrt(s + 5)  # Define the function to integrate

# 4th: Perform the integration with respect to 's'
integral_result = sp.integrate(integrand, s)  # Compute the integral

# 5th: Display the result
print(integral_result)  # Print the result of the integral

 

 

 

 

4. What is the python code for this problem:

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

# 2nd: Define the variable 't'
t = sp.symbols('t')  # Define the symbolic variable 't'

# 3rd: Define the integrand
integrand = t**2 * sp.sqrt(1 - t**2)  # Define the function to integrate

# 4th: Perform the integration with respect to 't'
integral_result = sp.integrate(integrand, t)  # Compute the integral

# 5th: Display the result
print(integral_result)  # Print the result of the integral

 

 

 

 

5. What is the python code for this problem:

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

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

# 3rd: Define the integrand
integrand = n**2 / sp.sqrt(n**2 - 4)  # Define the function to integrate

# 4th: Perform the integration with respect to 'n'
integral_result = sp.integrate(integrand, n)  # Compute the integral

# 5th: Display the result
print(integral_result)  # Print the result of the integral