If we have trial functions, which depend on n, of the form 6,n = x"exp(-ax). We are interested in being able to perform integrals (for any values of n, m and p) of the form: too dxó, (x)x² óm(x) = dra"+m+Pexp(-2ax²). (3) To perform these integrations we introduce the following integral and then employ integra- tion by parts to develop a recursion relation: rtoo I (2a) = | ) = / dez*erp{-2ar") (4) 1. If u = x2k-1 what is du? 2. If dv = xexp(-2ax²)dx, what is v? 3. What is the value of uv at x = 0? What is the value of uv at x = -oo? 4. What is the value of I-1(2a) in terms of I(2a)? k I(2a) (m,p,n) 1 2 TABLE I. Complete the table above by filling in the value of I(20)

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2A) Please answer the question completely and accurately with full detailed steps.
If we have trial functions, which depend on n, of the form ø,n = x"exp(-ax). We are
interested in being able to perform integrals (for any values of n, m and p) of the form:
rtoo
dra"+m+Pexp(-2ax²).
To perform these integrations we introduce the following integral and then employ integra-
tion by parts to develop a recursion relation:
rtoo
I (2a) =
) = /* dz*ezp(-2ar")
(4)
1. If u = x2k-1 what is du?
2. If dv = xexp(-2ax²)dx, what is v?
3. What is the value of uv at x = 0? What is the value of uv at x = -oo?
4. What is the value of I-1(2a) in terms of I(2a)?
k I(2a)
(m,p,n)
1
2
|(612*l61) = (øo]a*l60) = ($2\a²\&2) = (ø4|04)
TABLE I. Complete the table above by filling in the value of Ik(2a)
Transcribed Image Text:If we have trial functions, which depend on n, of the form ø,n = x"exp(-ax). We are interested in being able to perform integrals (for any values of n, m and p) of the form: rtoo dra"+m+Pexp(-2ax²). To perform these integrations we introduce the following integral and then employ integra- tion by parts to develop a recursion relation: rtoo I (2a) = ) = /* dz*ezp(-2ar") (4) 1. If u = x2k-1 what is du? 2. If dv = xexp(-2ax²)dx, what is v? 3. What is the value of uv at x = 0? What is the value of uv at x = -oo? 4. What is the value of I-1(2a) in terms of I(2a)? k I(2a) (m,p,n) 1 2 |(612*l61) = (øo]a*l60) = ($2\a²\&2) = (ø4|04) TABLE I. Complete the table above by filling in the value of Ik(2a)
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