Consider the definite integral I e -22 dx. (a) How big must we choose n so that the approximation of I by the midpoint rule is accurate to within .001? Justify your answer. You may leave your answer in calculator ready form. (b) Using that 1 „2n n! n=0 for all x, express I as an infinite sum. (c) How many terms of the above infinite sum are required to approximate I to within .001?
Consider the definite integral I e -22 dx. (a) How big must we choose n so that the approximation of I by the midpoint rule is accurate to within .001? Justify your answer. You may leave your answer in calculator ready form. (b) Using that 1 „2n n! n=0 for all x, express I as an infinite sum. (c) How many terms of the above infinite sum are required to approximate I to within .001?
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Transcribed Image Text:. Consider the definite integral
2
„2
I =
dx.
e
(a)
How big must we choose n so that the approximation of I by the midpoint rule is accurate
to within .001? Justify your answer. You may leave your answer in calculator ready form.
(b)
Using that
;(-1)"x2n
n=0
for all x, express I as an infinite sum.
(c)
How many terms of the above infinite sum are required to approximate I to within .001?
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