Numerical Methods

To apply Simpson’s three-eighth rule we use the given function values at the specified intervals and calculate the weighted sum The result of the integral is approximately 4.052985

Step 1: Use the Regula Falsi method.
The Regula Falsi method (or False Position method) is used to find roots of equations. It is an iterative method that uses the linear interpolation between two points to approximate the root. Given the equation and the interval , we calculate the initial approximations. Step 2: Apply the formula.
The formula for the next approximation is: Using the method, we find that the root is approximately . Final Answer: