(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

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter8: Further Techniques And Applications Of Integration
Section8.2: Integration By Parts
Problem 32E
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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 ==
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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