Solution Found!
Answer: 56 Use (a) the Midpoint Rule and (b) Simpsons Rule to approximate the given
Chapter 7, Problem 5(choose chapter or problem)
Use (a) the Midpoint Rule and (b) Simpson’s Rule to approximate the given integral with the specified value of \(n\). (Round your answers to six decimal places.) Compare your results to the actual value to determine the error in each approximation.
\(\int_{0}^{2} \frac{x}{1+x^{2}} d x, \quad n=10\)
Questions & Answers
QUESTION:
Use (a) the Midpoint Rule and (b) Simpson’s Rule to approximate the given integral with the specified value of \(n\). (Round your answers to six decimal places.) Compare your results to the actual value to determine the error in each approximation.
\(\int_{0}^{2} \frac{x}{1+x^{2}} d x, \quad n=10\)
ANSWER:Step 1 of 7
\(\int_{0}^{2} \frac{x}{1+x^{2}} d x, \quad n=10\)
Find the width of the intervals:
\(\Delta x=\frac{b-a}{n}=\frac{2-0}{10} \approx 0.2\)
Calculate the values at the midpoints of each interval.
\(f(x)=\frac{x}{1+x^{2}}\)