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 'y' y = sp.symbols('y') # Define the symbolic variable 'y' # 3rd: Define the integrand integrand = 1 / (16 + y**2) # Define the function to integrate # 4th: Perform the integration with respect to 'y' integral_result = sp.integrate(integrand, y) # Compute the integral # 5th: Display the result sp.pprint(integral_result) # 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 'w' w = sp.symbols('w') # Define the symbolic variable 'w' # 3rd: Define the integrand integrand = (w + 2) / sp.sqrt(4 - w**2) # Define the function to integrate # 4th: Perform the integration with respect to 'w' integral_result = sp.integrate(integrand, w) # Compute the integral # 5th: Display the result sp.pprint(integral_result) # 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 'y' y = sp.symbols('y') # Define the symbolic variable 'y' # 3rd: Define the integrand integrand = sp.exp(y) / (9 + 4 * sp.exp(2 * y)) # Define the function to integrate # 4th: Perform the integration with respect to 'y' integral_result = sp.integrate(integrand, y) # Compute the integral # 5th: Display the result sp.pprint(integral_result) # 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 't' t = sp.symbols('t') # Define the symbolic variable 't' # 3rd: Define the integrand integrand = 1 / sp.sqrt(4 * t - 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 sp.pprint(integral_result) # 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 's' s = sp.symbols('s') # Define the symbolic variable 's' # 3rd: Define the integrand integrand = s / (s**2 - 2*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 sp.pprint(integral_result) # Pretty print the result