66–71. {Use of Tech} Estimating error Refer to Theorem 8.1 in the following exercises.
68. Let f(x) = e^(x²).
d. Use Theorem 8.1 to find an upper bound on the absolute error in the estimate found in part (a).

64. (Use of Tech) Normal distribution of movie lengths

A study revealed that the lengths of U.S. movies are normally distributed with a mean of 110 minutes and a standard deviation of 22 minutes. This means that the fraction of movies with lengths between a and b minutes (with a < b) is given by the integral:

(1/(22√(2π))) ∫[a to b] e^(-((x-110)/22)²/2) dx.

What percentage of U.S. movies are between 1 hr and 1.5 hr long (60-90 min)?

66–71. {Use of Tech} Estimating error Refer to Theorem 8.1 in the following exercises.

66. Let f(x) = cos(x²).

d. Use Theorem 8.1 to find an upper bound on the absolute error in the estimate found in part (a).

66–71. {Use of Tech} Estimating error Refer to Theorem 8.1 in the following exercises.

67. Let f(x) = √(x³ + 1).

d. Use Theorem 8.1 to find an upper bound on the absolute error in the estimate found in part (a).

66–71. {Use of Tech} Estimating error Refer to Theorem 8.1 in the following exercises.

68. Let f(x) = e^(x²).

a. Find a Trapezoid Rule approximation to ∫[0 to 1] e^(x²) dx using n = 50 subintervals.

66–71. {Use of Tech} Estimating error Refer to Theorem 8.1 in the following exercises.

69. Let f(x) = sin(eˣ).

d. Find an upper bound on the absolute error in the estimate found in part (a) using Theorem 8.1.

66–71. {Use of Tech} Estimating error Refer to Theorem 8.1 in the following exercises.

70. Let f(x) = e^(-x²).

a. Find a Simpson's Rule approximation to the integral from 0 to 3 of e^(-x²) dx using n = 30 subintervals.

66–71. {Use of Tech} Estimating error Refer to Theorem 8.1 in the following exercises.

71. Let f(x) = √(sin x).

a. Find a Simpson's Rule approximation to the integral from 1 to 2 of √(sin x) dx using n = 20 subintervals.

66–71. {Use of Tech} Estimating error Refer to Theorem 8.1 in the following exercises.

71. Let f(x) = √(sin x).

b. Find an upper bound on the absolute error in the estimate from part (a) using Theorem 8.1. (Hint: |f''''(x)| ≤ 1 on [1,2].)