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(b) ∞ 2 X 2 2 (8x² - 12x) dx -∞

(b) ∞ 2 X 2 2 (8x² - 12x) dx -∞

Calculus: Early Transcendentals
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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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: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
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 ∞
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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