Solution Found!
Answer: Estimating IntegralsThe instructions for the
Chapter 8, Problem 3E(choose chapter or problem)
Problem 3E
Estimating Integrals
The instructions for the integrals in Exercises 1–10 have two parts, one for the Trapezoidal Rule and one for Simpson’s Rule.
I. Using the Trapezoidal Rule
a. Estimate the integral with n = 4 steps and find an upper bound for
b. Evaluate the integral directly and find
c. Use the formula (/( true values)) × 100 to express as a percentage of the integral’s true value.
II. Using Simpson’s Rule
a. Estimate the integral with n = 4 steps and find an upper bound for
b. Evaluate the integral directly and find
c. Use the formula (/( true values)) × 100 to express as a percentage of the integral’s true value.
Questions & Answers
QUESTION:
Problem 3E
Estimating Integrals
The instructions for the integrals in Exercises 1–10 have two parts, one for the Trapezoidal Rule and one for Simpson’s Rule.
I. Using the Trapezoidal Rule
a. Estimate the integral with n = 4 steps and find an upper bound for
b. Evaluate the integral directly and find
c. Use the formula (/( true values)) × 100 to express as a percentage of the integral’s true value.
II. Using Simpson’s Rule
a. Estimate the integral with n = 4 steps and find an upper bound for
b. Evaluate the integral directly and find
c. Use the formula (/( true values)) × 100 to express as a percentage of the integral’s true value.
ANSWER:
SOLUTION:
Step 1 of 7:
In this question,
I. Using the Trapezoidal Rule
a. Estimate the integral with n = 4 steps and find an upper bound for
b. Evaluate the integral directly and find
c. Use the formula (/( true values)) × 100 to express as a percentage of the integral’s true value.
II. Using Simpson’s Rule
a. Estimate the integral with n = 4 steps and find an upper bound for
b. Evaluate the integral directly and find
c. Use the formula (/( true values)) × 100 to express as a percentage of the integral’s true value.