Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:Gaussian functions
G.1
G.2
G.3
G.4
G.5
G.6
G.7
G.8
8
S
8
0
e-ax²
8
1
[["new" daw !
dx=
0
2a
dx=
8
[x²e-dx-1(5)
x²e-ax² dx =
4
1 T
erfz=
8
S™
0
11
S x³e-ax² dx=
0
0
2 a
2
3
[x²e-max->()"
x¹e-ax² dx=
1
2q²
So
1/2
1/2
e-x² dx
1/2
TC¹
m!
x²
₂2m+1e¬ax² dx =
2qm+1
x²me-ax² dx =
1/2
erfc z=1-erf z
(2m-1)!! T
2m+1 am
(2m-1)!!=1×3×5...×(2m-1)
(1)
a
1/2

Transcribed Image Text:Using the even- or odd-ness of the
following functions and the integral table
evaluate each of the following
integrals. (Clearly identify the integral form and
"a" value.)
(b) † (8x² − 12x)e#dx
∞
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