Chapter 8.8, Problem 48E

a.

To determine

To find: The value of the integral ${\displaystyle {\int }_0^{\frac{\pi }{4}}\frac{dx}{1+x^2}}$ with the help of Trapezoid rule approximation.

b.

To determine

To find: The value of the integral ${\displaystyle {\int }_0^{\frac{\pi }{4}}\frac{dx}{1+x^2}}$ with the help of Simpson’s rule approximation.

c.

To determine

To compute: The absolute errors in the Trapezoid Rule and Simpson’s Rule with 2n subintervals.