Mathematics, 25.02.2020 04:36, ShianHagen5
(a) Use the Midpoint Rule, with n=4, to approximate the integral ∫7e^−x2 dx (with boundaries a=0 and b=4).
M4= aws (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 TI83/84 or 2ND 7 on the TI-89.∫7e^−x2 dx= (with boundaries a= 0 and b=4).
(c) The error involved in the approximation of part (a) is
EM=∫7e^−x2 dx−M4= anw.
(d) The second derivative f′′(x)= anw .
The value of K = max |f′′(x)| on the interval [0, 4] =anw .
(e) Find a sharp upper bound for the error in the approximation of part (a) using the Error Bound Formula |EM| ≤K(b−a)^3\ 24n^2= (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 "Mn" to the integral is guaranteed to be accurate to within 0.001.
Answers: 2
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(a) Use the Midpoint Rule, with n=4, to approximate the integral ∫7e^−x2 dx (with boundaries a=0 and...
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