Solution Found!
Comparing the Midpoint and Trapezoid Rules Compare the
Chapter 5, Problem 40E(choose chapter or problem)
Comparing the Midpoint and Trapezoid Rules Compare the errors in the Midpoint and Trapezoid Rules with n=4, 8, 16, and 32 subintervals when they are applied to the following integrals (with their exact values given).
\(\int_{0}^{\pi / 2} \sin ^{6} x d x=\frac{5 \pi}{32}\)
Questions & Answers
QUESTION:
Comparing the Midpoint and Trapezoid Rules Compare the errors in the Midpoint and Trapezoid Rules with n=4, 8, 16, and 32 subintervals when they are applied to the following integrals (with their exact values given).
\(\int_{0}^{\pi / 2} \sin ^{6} x d x=\frac{5 \pi}{32}\)
ANSWER:Solution:-
Step1
Given that
Compare the errors in the Midpoint and Trapezoid Rules with n =4, 8, 16, and 32 subintervals
n = 4,8, 16, and 32
The exact values of the integrals are given for computing the error.
dx= 0.490874
Step2
To find
Compare the errors in the Midpoint and Trapezoid Rules with n =4, 8, 16, and 32 subintervals when they are applied to the following integrals (with their exact values given).
Step3
a=0 , b=1.5708, n=4
Using midpoint rule
Step4
Midpoint sum for N=4
+
+-------+
)
+
+-------+
)
=0.490874
Error for N=4 for midpoint rule
=
=
=1.348
Step5
Using midpoint rule
Midpoint sum for N=8
+
+-------+
)
+
+-------+
)
=0.490874
Error for N=8 for midpoint rule
=
=
=2.57919
Step6