Introduction Notes Theory HOWTO Examples Engineering Error Questions Matlab Maple

Question 1

Approximate the integral of f(x) = e^-x on [0, 10] with 20 subintervals.

Answer: 1.02070069942442

Question 2

Approximate the integral of f(x) = e^-x on [0, 10] starting with one interval and continuing until the difference between two approximations (ε_step) is less than 0.000001.

Answer: after 13 iterations, we get 0.999954724240937

Question 3

Approximate the integral of f(x) = x² on the interval [-2, 2] with 4 and 8 intervals.

Answer: 6 and 5.5

Question 4

What is the estimated error (using the mean of the 2nd derivative) for the approximate in Question 3 when using eight intervals and what is the actual error?

Answer: the estimated and actual errors are equal -1/6 because the second derivative of x² is 2.

Question 5

Approximate the integral of f(x) = x⁴ on the interval [-2, 2] with 4 and 8 intervals.

Answer: 18 and 14.125

Question 6

What is the estimated error for the approximate in Question 5 when using eight intervals and what is the actual error?

Answer: the estimated of the error is -1.3333333 whereas the actual error is -1.325⋅⋅⋅.