Use the Trapezoidal Rule the Midpoint Rule and Simpsons Rule

Use the Trapezoidal Rule, the Midpoint Rule, and Simpson\'s Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) the Trapezoidal Rule, the Midpoint Rule, Simpson\'s Rule

Solution

h=0.5-0/4=1/8 A)Trapezoidal I= (h/2)[ f(0)+f(1/2)+2(f(1/8)+f(1/4)+f(3/8))] =(5/16)[0+0.2376+2(0.015+0.06+0.1345)] =0.205 B) Midpoint I=h[f(1/16)+f(3/16)+f(5/16)+f(7/16)] =(5/8)[0.0038+0.034+0.0935+0.1827] =0.314 C)Simpson I=h/6[f(0)+f(1/2)+4(f(1/8)+f(1/4)+f(3/8))] =(5/48)[0+0.2376+4(0.015+0.06+0.1345)] =0.112