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Engineering Error Questions Matlab Maple
Question 1
Approximate the integral of f(x) = e-x on [0, 10] using the trapezoidal rule.
Answer: 5.00022699964881
Question 2
Approximate the integral of f(x) = x2 on the interval [0, 2] using the trapezoidal rule.
Answer: 4
Question 3
What is the estimated error (using the mean of the 2nd derivative) for the approximate in Question 2 when using eight intervals and what is the actual error?
Answer: the estimated and actual errors are equal −4/3 because the second derivative of x2 is 2.
Question 4
Approximate the integral of f(x) = x4 on the interval [0, 2] using the trapezoidal rule.
Answer: 16
Question 5
What is the estimated error for the approximation in Question 4 what is the actual error?
Answer: the estimated of the error is −32/3 = −10.6667 whereas the actual error is −48/5 = −9.6 .
Copyright ©2005 by Douglas Wilhelm Harder. All rights reserved.
