Question

In estimating ∫₋₁²cos (3 x) d x using Trapezoidal and Simpson's rule with n=10, we can estimate the error involved in the approximation using the Error Bound formulas.

Answer 1

To estimate the integral using Trapezoidal and Simpson's rule, divide the interval and calculate the sum of areas of trapezoids. Use Error Bound formulas for estimating the error.

Step-by-step explanation:

To estimate the integral ∫₋₁²cos (3 x) d x using Trapezoidal and Simpson's rule with n=10, we can first divide the interval [-1, 2] into 10 subintervals.

Then, we can use the Trapezoidal rule to approximate the integral by calculating the sum of the areas of trapezoids formed by each pair of adjacent points on the graph of the function.

The error involved in the approximation can be estimated using the Error Bound formulas for Trapezoidal and Simpson's rule.