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.

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.

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).

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].)

95–98. {Use of Tech} Numerical integration Estimate the following integrals using the Midpoint Rule M(n), the Trapezoidal Rule T(n), and Simpson’s Rule S(n) for the given values of n.

96. ∫ (from 1 to 3) dx/(x³ + x + 1); n = 4