(a) Use the Midpoint Rule, with n=4, to approximate the integral fo Tedz. (Round your answers to six decimal places) M₁ 0.75123 (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. Te dir= 6.20354 (c) The error involved in the approximation of part (a) is EM= Tedz-M₁ 0.1349 (d) The second derivative f" (2) AveN-x^/211-264-x71211
(a) Use the Midpoint Rule, with n=4, to approximate the integral fo Tedz. (Round your answers to six decimal places) M₁ 0.75123 (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. Te dir= 6.20354 (c) The error involved in the approximation of part (a) is EM= Tedz-M₁ 0.1349 (d) The second derivative f" (2) AveN-x^/211-264-x71211
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![(a) Use the Midpoint Rule, with 714, to approximate the integral Tedz.
(Round your answers to six decimal places)
M₁
0.75123
(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. f7edie =
6.20354
(c) The error involved in the approximation of part (a) is
EM= 7e'da-M₁ 0.1349
(d) The second derivative f" (a)= 4xe^(-x^(2))-20^(-x^(2))
The value of K-max [f" (a) on the interval [0, 4] 2
(e) Find a sharp upper bound for the error in the approximation of part (a) using the Error Bound Formula EMK(-a)²
24²
0.3334
(where a and b are the lower and upper limits of integration, the number of partitions used in part a).
(f) Find the smallest number of paons n so that the approximation M,, to the integral is guaranteed to be accurate to within 0.001.
73
n ==](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F30f34acc-cb1c-4cb7-8199-d8fd5748a2a6%2F512cc528-b20e-42f6-b362-1e86f39e40c4%2Fzu3rznn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) Use the Midpoint Rule, with 714, to approximate the integral Tedz.
(Round your answers to six decimal places)
M₁
0.75123
(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. f7edie =
6.20354
(c) The error involved in the approximation of part (a) is
EM= 7e'da-M₁ 0.1349
(d) The second derivative f" (a)= 4xe^(-x^(2))-20^(-x^(2))
The value of K-max [f" (a) on the interval [0, 4] 2
(e) Find a sharp upper bound for the error in the approximation of part (a) using the Error Bound Formula EMK(-a)²
24²
0.3334
(where a and b are the lower and upper limits of integration, the number of partitions used in part a).
(f) Find the smallest number of paons n so that the approximation M,, to the integral is guaranteed to be accurate to within 0.001.
73
n ==
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