Estimate for the trapezoidal rule to give a bound for the

Question

1. We know it Π = 4 Arctan(1) = 4 ₀∫¹ 1/ (1 + x²)dx. Use the Trapezoidal rule and Simpson's rule to approximate the integral with n = 6.

What estimates for Π do you obtain?

2. Use the error estimate for the Trapezoidal rule to give a bound for the error in problem A for the Trapezoidal rule.

3. Use the error estimate for the Trapezoidal rule to determine a value n, so that the error is less than 10^-2.