- 2 Points Book Problem 18 A Use The Trapezoidal Rule With N 5 To Approximate The Integral 7 Cos 4x Dx T5 1 1 (75 KiB) Viewed 46 times
(2 points) (a) Use Simpson's Rule, with n = 6, to approximate the integral ¹7e-2ª da. S6 = 3.026531361725054 (b) The actual value of f¹7e-2x dx = (7/2)(1-(1/e^2)) (c) The error involved in the approximation of part (a) is Es ¹7e-2x dx - S6 = (d) The fourth derivative ƒ(4) (x) = The value of K = max |ƒ(4) (x)| on the interval [0, 1] = K(b-a)³ (e) Find a sharp upper bound for the error in the approximation of part (a) using the Error Bound Formula Es| < 180n4 (f) Find the smallest number of partitions n so that the approximation S, to the integral is guaranteed to be accurate to within 0.0001. n =
(1 point) Book Problem 20 Find the smallest number of partitions n so that the approximation to f₁5 In xdx using Simpson's Rule is accurate to within 0.0001? Answer: n =
(2 points) Book Problem 17 (a) Use the Midpoint Rule, with n = 4, to approximate the integral ₁7e-ª²³ dx. M₁ = 6.202947 (Round your answers to six decimal places.) (b) Compute the value of the definite integral in part (a) using your calculator, such as MATH 9 on the T183/84 or 2ND 7 on the TI-89. f47e-ª³² dx = 6.203588383 (c) The error involved in the approximation of part (a) is EM = 7e-¹² dx - M₁ = 6.41383E-4 (d) The second derivative f"(x) = The value of K = max |f" (x)| on the interval [0, 4] = K(b-a)³ 24n² (e) Find a sharp upper bound for the error in the approximation of part (a) using the Error Bound Formula EM < (where a and b are the lower and upper limits of integration, n the number of partitions used in part a). (f) Find the smallest number of partitions n so that the approximation M, to the integral is guaranteed to be accurate to within 0.001. n =